Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
@MathQueenSusanne Liked and followed. Second video I saw from you this week. Best and simple explanation ever! Love that you run thru why, in each step and repeat basic rules. All the details one forget after a while. Fantastic way to teach math if one needs to refresh knowledge! 💪🏻💪🏻
I love how you not only teach how to solve math problems, but also explain the fundamentals behind them. You do this in a simple and easy-to-understand way. thanks for video
What fundamentals here did she give? 0:25 on. Better to say to the viewer first: "What is a log? Why do we use them and how? All a log is an exponent of a base number (usually 2, 10, or e) to arrive at another number, such as 16. We convert numbers to logarithms, historically, to speed up multiplication, since when we multiply numbers to the same base raised to an exponent we only need add the exponents. So to find the log of 16 to the more common base 2 we ask what power must 2 be raised to to equal 16? 2x2x2x2 = 16, so 2 to the 4th power, so it is = 4; now for this question of base 4, we asked the same question of 4 and we get 2, mindful that base 4 is not common in real life logs." That is how to teach the viewer to understand to point better, I submit; less reliance of rote steps; don't assume everyone knows why we even use logs today given calculators or their fundamentals.
It's been about 50 or 55 years since I directly applied this math, however, your clear instruction was the review I needed for it all to come back crystal clear!
Hey, Susanne, I am a retired teacher and have not done logs for 20 years. You surprised me with these in that I missed one, but picked up the skill with this video. Love 😍😍
So glad your channel popped up in my Recommendations a week or so ago. I've always had a love of maths but have found that every teacher I've had at school went slightly too fast for me to keep up. The pace of your videos is perfect for me.
My bachelor’s degree is math, and my other degrees required considerable math applications as did my career. I am 76 years old and retired and I really enjoy your channel as it helps keep my mind active, and it also helps me remember old knowledge I had forgotten. You may have nudged me to volunteer to tutor students having trouble with math (as long as it’s not partial differential equations).
Thank you very much for the examples and solutions. What’s beautiful about your approach is that you sense and empathize with our difficulty in solving😊
It's nice that you make these videos. They are really good. But are the only people who listen to it the same people that already know the answer? Your explanations are great. Get them to those who don't have those skills.
Thanks for your thorough explanations on higher math! Not having a college degree, I took a basic algebra course to enter the electronics field. The instructor was not good at explaining polynomials as I recalled. Hope you have 100000 subscribers soon!
She already has 600k+ subs on her german channel "Mathematrick" :) But yeah, hopefully her videos gets also popular on the global market. Btw, Susanne also has a metal band called MoonSun. Something between symphonic and power metal. They have done many great covers and have some originals as well. She has an outstanding singing voice.
I really love you videos so often in math videos they skip steps as if they are just common know page and end up pulling numbers out their ass but you explain every step and are much easier to follow
For Reasons, I missed this type of math in High School and was expected to know it when at college. I muddled through it by rote. It's nice to have some understanding of it!
You can evaluate any decimal log mentally in a few seconds, as long as a limited precision is acceptable. Using my method, I can get 3 decimals of precision in 5~10s for the log of any number. Needless to say, if you learn how to calculate logs and antilogs mentally, you will also soon be able to calculate any powers/roots, large multiplications/divisions, base changes, and some simple Taylor expansions (for example for trig) with minimal effort (I can do most of these with errors of 0.1~1% within 20s~1min). The starting point is to memorize a short list of logs (similarly to how you memorized the multiplication boards, as a kid). This list consists of the logs of simple numbers (1~9) and the logs of small increments (-10% ~ +10% -- note that the log of small increments is approximately linear, so you can easily eyaball intermediate values!). Then, to calculate the log of any number, all you have to do is decompose it into a simpler number plus a small increment, calculate both logs and add them up. This gives you the fractional part of the log; the integer part you get directly from the magnitude of the number. Yes, it really is that simple... ---------------------------------------- We can do a quick RNG example, so that you can see my method in practice: calculate log(4963) 1) Ignoring the magnitude, we have 4.963 = 5 - 0.037 ~= 5 - 0.75% 2) log(5) ~= 0.699; log(-0.75%) ~= -0.0033 --> from here, the fractional part is given by 0.699 - 0.0033 = 0.6957 3) Looking at the magnitude, 4963 is in the thousands, so the integer part is 3 --> log(4963) ~= 3.6957 (Real value: 3.695744275....). Pretty accurate and not really rocket science, as you can see! ---------------------------------------- Here is the list of logs I learned by heart. I use 3 decimals because it strikes the sweetspot between accuracy and mental load. NOTE 1: I memorize these values without the decimals (for example, log(5) I memorize as 699 instead of 0.699) because it reduces the computational load and makes it easier to avoid mixing up orders of magnitude (for example, I find 0.0043 and 0.043 easier to mix up than 4.3 and 43). NOTE 2: Many of the items in this list can be derived directly from each other, like log(4) = 2 * log(2). This means that, at first, you won't even need to memorize the full list -- but this will come at the cost of increasing your mental load. In fact, if you know log(+1%), you can derive all other logs in the list from it with more or less work -- I will let you figure that one out by yourself, but feel free to drop me a comment if you are struggling with some cases. 2 --> .301 6 --> .778 3 --> .477 7 --> .845 4 --> .602 8 --> .903 5 --> .699 9 --> .954 -1% --> -.0044 +1% --> +.0043 -5% --> -.022 +5% --> +.021 -10% --> -.046 +10% --> +.041
We had to learn this by heart in 8th grade in India - "THE LOGARITHM OF A NUMBER FOR A GIVEN BASE IS THE INDEX TO WHICH THE BASE MUST BE RAISED TO PRODUCE THAT NUMBER" .
10:08 Or you can flip 36 to (1/36)^(-1), move -1 in front of the logarithm and proceed as usual. Thus, we discovered the identity log(a,x) = -log(a,1/x).
4:37 that is shallow rote learning, though; better to see that we only need to factor 27 get 3 cubed; then when we square that we go from three 3's to six 3's; better to see it, so it makes sense first without the rote move. So the question asks what is the exponent of 3 that equals six 3's multiplied together? 6.
Thank you so much for this tutorial, bc I never knew you could do logarithms by hand. Any math class I had that involves logarithm calculations, the math teacher said there is no shorthand to logs and they must be down by calculator, sooo that definitely says a lot about America tbh
If only my math teachers in middle and high school were half as good as you math would not have been the bitter, unpleasant experience it was. Instead it was left to me to teach myself, a challenge I accepted and eventually overcame with A grades in College Algebra and Calculus. Your kind, crystal clear presentations are a joy and a delight. They remind me gifted teachers can make subjects we find daunting understandable. Please keep up the good work.
You have great teaching skills and selected very good examples. I just think the negative log example should've been the last one, because it is the trickiest to "imagine". Negative power is something not very natural to most people.
8:39 how is it "always a 10"? In computer science it might be a 2 by convention or a 16, which are more common for machine language applications. In engineering it may be base e, called the 'natural log' (Euler).
This is math that I never learned. A giant THANKS and 2 Thumbs Up for this revelation. P.S. I hope you do some videos on statistics. To me, this was the most poorly math taught.
8:19 In speech, "logarithm" by itself (no base specified) is often taken by mathematicians to refer to the natural logarithm (base e). But Susanne is of course correct to say that "log," when written without a base, is almost always understood to imply the base-10 logarithm.
Hi Suzanna, Roland from Venray, NL here. I've seen some of your video's the last couple of days. Before I saw comparable videos of, primarily (BTW brilliant) Indian guys, but, although the steps they followed were correct, I missed the 'whys' and 'whens', whereas you explain in an almost childish manner (not an offence; a compliment!!!) how to solve such problems. Chapeau! (If you're not familiar with French: Hats off!)
Hi Roland, thank you so much for your kind words! We actually learn French at school in Germany and this is me 11 years ago: ua-cam.com/video/XqBy8ftwCcM/v-deo.htmlsi=nD-yVSsAC6iEv5ou
@MathQueenSusanne Also kann ich auch auf Deutsch mit dir reden. Werde ich aber nicht mehr tun, weil viele anderen Leute es nicht verstehen würden. Übrigens: Schone stimme und auch noch piano-fähig! Großartig!
My math book said: log (2) 16 = 4 because 16 = 2 raised to the 4th power. That was it, no further explanation. I have an easy time understanding math, but I have an even easier time with your explanation.
While I LOVE your videos, I must admit, everything after "Hello my lovelies" was WAAYYYY above my paygrade ;-) Although I do hope something you said will creep into my feeble mind!!!
@wheechie Microslop didn't make it any easier with their choice of integer basis for universe date either. Who da phuq has 1900-01-01 at midnight as their universe date?
Nice video and great examples increasing in difficulty, but i was waiting for when the answer didn't round out so nicely. It didnt come. For example, what if the last one was Log 2/3 of 16/80?
For the cases where you had a log of 1/n that is the same as n to the power of -1. You move the -1 to the front then you have negative log of n. It skips that expansion you did where you wind up with a term of 0. You can use that same identity when dealing with a fractional base. EDIT: The other way to do logs without a calculator is to use a slide rule. :)
The reason any base to the power of zero is one which means log 1 = 0 for any base, can be shown like this. Division requires exponents be subtracted. n^x/n^x = 1 n^x/n^x = n^(x-x) = n^0 So, n^0 = 1 It is a provable fact and does not rely on the old, "we define it that way.
You say "we have to count how often we have mutiplied ..." but the relevant number here is not the number of multiplications but the number of factors, which is the number of multiplications plus one.
I had a "nightmare" teacher who would make up the test questions, off the top of his head, at the beginning of class. You might get craziness like, log 0.003 or log 11. The book had nice, neat answers, like yours. His could be some horrifying fraction, or even no solution, at all. A couple of times, even he said, "Ooh, this was a bad question," as he struggled to solve it. His motto was: Use your tools; Work the problem.
What do we do when the numbers are not so nice, such as log (base 10) 1100 If'ns I was to guess, I'd say we factor the 1100 into 1000 * 1.1 so log(1000)+log(1.1), then treat log(1.1) as log(11/10) ? But with the method shown, log(11/10) = log(1)...
With base 10 all you have to remember is log(2)=~0.3, log(3)=~0.48 and log(7)~=0.85. All the others are either trivial or combinations of those 3: log(1) = 0, easy to remember as is log(10) = 1 log(4) = log(2 * 2) = 0.3 + 0.3 = 0.6 log(5) = log(10 / 2) = 1 - 0.3 = 0.7 log(6) = log(2 * 3) = 0.3 + 0.48 = 0.78 log(8) = log(2 * 2 * 2) = 0.3 + 0.3 + 0.3 = 0.9 log(9) = log(3 * 3) = 0.48 * 0.48 = 0.96 With that you can raise any number to any power (or find any root of any number) with surprising accuracy by reducing the number to the 0-1 range (keeping the exponent in mind), using basic linear interpolation between the known values in that range to get the log of your base, dividing or multiplying by the power/index and then repeating the process in reverse to find the inverse log, which in turn gives you your final answer. Requires a bit of practice, but can certainly be done in your head if you have some basic math skills.
4:44 this is probably a stupid question but instead of moving the power of 2 to the front of the Log why not just operate 27^2 and then resolve the logarithm
hhhhhhhhh good method and here is another method log ( 2/3 ; 16/81) = log( 16/81) / log (2/3) = log ( 2^4 /3^4) /log( 2/3) = log ((2/3)^4)) / log(2/3 ) = (4 log(2/3)) / log(2/3) = 4 ps : c'est une très bonne méthode pour expliquer le calcul des logarithmes mais il ne faut pas oublier que seuls 3 logarithmes sont les plus utilisés 1- log (10 ; x ) = log x .........( la notation admise 2- log ( e ; x ) = Ln x = Log x ........( la notation admise 3- log (2 ; x ) = log (2 ; x) .........( la notation admise
Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
I love your program. What is it? "Fans only" for nerds?
@MathQueenSusanne
Liked and followed. Second video I saw from you this week. Best and simple explanation ever! Love that you run thru why, in each step and repeat basic rules. All the details one forget after a while. Fantastic way to teach math if one needs to refresh knowledge! 💪🏻💪🏻
HOw di dyou get 22K subscribers in a month?
I love how you not only teach how to solve math problems, but also explain the fundamentals behind them. You do this in a simple and easy-to-understand way. thanks for video
Yes. I am learning all kinds of stuff I never quite grasped at school.
Wow,can I be learn from you
What fundamentals here did she give? 0:25 on.
Better to say to the viewer first: "What is a log? Why do we use them and how? All a log is an exponent of a base number (usually 2, 10, or e) to arrive at another number, such as 16. We convert numbers to logarithms, historically, to speed up multiplication, since when we multiply numbers to the same base raised to an exponent we only need add the exponents. So to find the log of 16 to the more common base 2 we ask what power must 2 be raised to to equal 16? 2x2x2x2 = 16, so 2 to the 4th power, so it is = 4; now for this question of base 4, we asked the same question of 4 and we get 2, mindful that base 4 is not common in real life logs." That is how to teach the viewer to understand to point better, I submit; less reliance of rote steps; don't assume everyone knows why we even use logs today given calculators or their fundamentals.
Math Queen, thank you for making mathematics accessible to this old geezer after I fled from the subject for decades. It's a miracle. 🤩
It's been about 50 or 55 years since I directly applied this math, however, your clear instruction was the review I needed for it all to come back crystal clear!
Hey, Susanne, I am a retired teacher and have not done logs for 20 years. You surprised me with these in that I missed one, but picked up the skill with this video. Love 😍😍
A math teacher/mentor with a sense of humor, how refreshing!
specifically, what is it you found humorous about her? i think she might have bubbly personality, but that is not humorous.
I like that you don’t skip steps. Your videoa are really good for people who are really struggling.
So glad your channel popped up in my Recommendations a week or so ago. I've always had a love of maths but have found that every teacher I've had at school went slightly too fast for me to keep up. The pace of your videos is perfect for me.
My bachelor’s degree is math, and my other degrees required considerable math applications as did my career. I am 76 years old and retired and I really enjoy your channel as it helps keep my mind active, and it also helps me remember old knowledge I had forgotten. You may have nudged me to volunteer to tutor students having trouble with math (as long as it’s not partial differential equations).
That is awesome!
Thank you very much for the examples and solutions. What’s beautiful about your approach is that you sense and empathize with our difficulty in solving😊
It's nice that you make these videos. They are really good. But are the only people who listen to it the same people that already know the answer?
Your explanations are great. Get them to those who don't have those skills.
Very 😂good teacher. I am a grandma remembering my college mathematics.
Thank you. It is fun!
You born to be a teacher, you break the basics at best. No child can struggle with you
I like the repetition because it helps me to remember the steps to solve this type of math problem.Thanks!
The math queen is not only smart but beautiful.
Keep sharing your knowledge and passion.
I thought so too.. she was paid for her beautiful voice. that's it!
I'd prefer a hot Math King.
You are a great teacher.
100 %
I wish I had logarithms explained to me like you did in this video. I wouldn’t have struggled with them. Thanks so much for this 👍
I like how you represent logarithms to evaluate them. I constantly need to remind myself of the log relationship, well done.
It is wonderful going 15 years in the past with such a great explanation.
Thanks for your thorough explanations on higher math! Not having a college degree, I took a basic algebra course to enter the electronics field. The instructor was not good at explaining polynomials as I recalled. Hope you have 100000 subscribers soon!
She already has 600k+ subs on her german channel "Mathematrick" :) But yeah, hopefully her videos gets also popular on the global market. Btw, Susanne also has a metal band called MoonSun. Something between symphonic and power metal. They have done many great covers and have some originals as well. She has an outstanding singing voice.
Did you mean “100000 subscribers” or “10 to the 5th power subscribers”?
@@keithmills778 100k! Sharp comment.....
You tell it in a very nice and cheerful way. You are wonderful. I wish you success in your career.👏
Great channel, great material and great content. Thank you for being so detailed and patient.
Many thanks for the tilents and very good manner of solving the maths problems.
I really love you videos so often in math videos they skip steps as if they are just common know page and end up pulling numbers out their ass but you explain every step and are much easier to follow
Love this channel. It's great to revisit these mathematical lessons again after decades. As a bonus, the teacher's cute too. 😂
For Reasons, I missed this type of math in High School and was expected to know it when at college. I muddled through it by rote. It's nice to have some understanding of it!
Since you capitalized _reasons_ and _high school,_ I'm surprised that you didn't also capitalize _college._
@@herrickinman9303 wow so insightful!
log(2 ; 1/8) = log (1/8) / log2
= (log1 - log8) / log2 = (0 - log8) / log2 = - log(2^3) / log2 = -3 log2 / log2 = -3
Thanks Queen !
You've just burned my brain cells lol
@@toby9999
log(a ; x) = log x / log a
Since 1/8 = 2^(-3), we have log2 (1/8) = log2 (2^(-3)) = -3.
Thank you. Great teaching manner. I look forward to studying further video lessons.
Excellent presentation, clear, engaging and thorough. Thank you very much.
Thank you for your beautifully clear exposition of these logarithmic examples.
Your explanation is superb. Thanxs for helping explaining rusty math problem to my kids.
You can evaluate any decimal log mentally in a few seconds, as long as a limited precision is acceptable. Using my method, I can get 3 decimals of precision in 5~10s for the log of any number. Needless to say, if you learn how to calculate logs and antilogs mentally, you will also soon be able to calculate any powers/roots, large multiplications/divisions, base changes, and some simple Taylor expansions (for example for trig) with minimal effort (I can do most of these with errors of 0.1~1% within 20s~1min).
The starting point is to memorize a short list of logs (similarly to how you memorized the multiplication boards, as a kid). This list consists of the logs of simple numbers (1~9) and the logs of small increments (-10% ~ +10% -- note that the log of small increments is approximately linear, so you can easily eyaball intermediate values!). Then, to calculate the log of any number, all you have to do is decompose it into a simpler number plus a small increment, calculate both logs and add them up. This gives you the fractional part of the log; the integer part you get directly from the magnitude of the number. Yes, it really is that simple...
----------------------------------------
We can do a quick RNG example, so that you can see my method in practice: calculate log(4963)
1) Ignoring the magnitude, we have 4.963 = 5 - 0.037 ~= 5 - 0.75%
2) log(5) ~= 0.699; log(-0.75%) ~= -0.0033 --> from here, the fractional part is given by 0.699 - 0.0033 = 0.6957
3) Looking at the magnitude, 4963 is in the thousands, so the integer part is 3
--> log(4963) ~= 3.6957 (Real value: 3.695744275....). Pretty accurate and not really rocket science, as you can see!
----------------------------------------
Here is the list of logs I learned by heart. I use 3 decimals because it strikes the sweetspot between accuracy and mental load.
NOTE 1: I memorize these values without the decimals (for example, log(5) I memorize as 699 instead of 0.699) because it reduces the computational load and makes it easier to avoid mixing up orders of magnitude (for example, I find 0.0043 and 0.043 easier to mix up than 4.3 and 43).
NOTE 2: Many of the items in this list can be derived directly from each other, like log(4) = 2 * log(2). This means that, at first, you won't even need to memorize the full list -- but this will come at the cost of increasing your mental load. In fact, if you know log(+1%), you can derive all other logs in the list from it with more or less work -- I will let you figure that one out by yourself, but feel free to drop me a comment if you are struggling with some cases.
2 --> .301 6 --> .778
3 --> .477 7 --> .845
4 --> .602 8 --> .903
5 --> .699 9 --> .954
-1% --> -.0044 +1% --> +.0043
-5% --> -.022 +5% --> +.021
-10% --> -.046 +10% --> +.041
That's spectacular
As a fellow math(s) educator, I appreciate the enthusiasm you show for "our" subject! 😃
She loves math, that is why. She very pleasant to listen to and she is also an educated person.
I look forward to watching all your videos. I had no idea what log was. And these helped me a lot.
very nice & smooth work
love your teaching style ❤
Super-summary:
"2 to what power is 1/8?
"Let's see 1/8 = 1/(2^3) = 2^(-3). So the power is -3!!!
We had to learn this by heart in 8th grade in India - "THE LOGARITHM OF A NUMBER FOR A GIVEN BASE IS THE INDEX TO WHICH THE BASE MUST BE RAISED TO PRODUCE THAT NUMBER" .
Somehow with caps this makes so much more sense. Nice!
I'm still struggling to visualise that
Just found your site and subscribed. Love the clarity of your explanations and that you use many examples.
10:08 Or you can flip 36 to (1/36)^(-1), move -1 in front of the logarithm and proceed as usual. Thus, we discovered the identity log(a,x) = -log(a,1/x).
A wonderful way of explaining logs. 🤸🎉 Thank you Math Queen and season greetings.
Very good video Lester. After a disappointing start you pulled it back nicely. You never give up which is a lesson to us all. Well done
Uma aula deliciosa de logaritmos! Vc explica muito bem mesmo! Parabéns!
With all the math you are showing me, I think you should be called the Math goddess instead of the Math Queen.
Or Math Empress?
Thank you
Teacher Maths Simplified
4:37 that is shallow rote learning, though; better to see that we only need to factor 27 get 3 cubed; then when we square that we go from three 3's to six 3's; better to see it, so it makes sense first without the rote move. So the question asks what is the exponent of 3 that equals six 3's multiplied together? 6.
You showed me how to solve my life problems not only math ❤
Thanks for this refresher. It has been a long time since I played with logs!
Welcome back!
Another great review. Thank you!
I'm loving your videos, the youtube algorithm did it again!
AWESOME job teach !! best ever simple and very well clarified...many thanks...for a GREAT job !!
Thank you so much for this tutorial, bc I never knew you could do logarithms by hand. Any math class I had that involves logarithm calculations, the math teacher said there is no shorthand to logs and they must be down by calculator, sooo that definitely says a lot about America tbh
You're totally amazing. Thanks!
Thanks a lot .
Very interesting.
Good luck
Really appreciate your teachings
If only my math teachers in middle and high school were half as good as you math would not have been the bitter, unpleasant experience it was. Instead it was left to me to teach myself, a challenge I accepted and eventually overcame with A grades in College Algebra and Calculus. Your kind, crystal clear presentations are a joy and a delight. They remind me gifted teachers can make subjects we find daunting understandable. Please keep up the good work.
You have great teaching skills and selected very good examples.
I just think the negative log example should've been the last one, because it is the trickiest to "imagine". Negative power is something not very natural to most people.
8:39 how is it "always a 10"? In computer science it might be a 2 by convention or a 16, which are more common for machine language applications. In engineering it may be base e, called the 'natural log' (Euler).
This is math that I never learned. A giant THANKS and 2 Thumbs Up for this revelation. P.S. I hope you do some videos on statistics. To me, this was the most poorly math taught.
8:19 In speech, "logarithm" by itself (no base specified) is often taken by mathematicians to refer to the natural logarithm (base e). But Susanne is of course correct to say that "log," when written without a base, is almost always understood to imply the base-10 logarithm.
So, is that why ln is used for base e?
A great way of understanding logarithms
Thank you so much for your assistance
Just l am surprising on your calculations !!! Wow so amazing !!
I like it.
Perfect explanation. Thanks
This channel is going to be big.
Mental arithmetic! 1/8 = 2 ^-3 Answer =-3 by definition
Wow, I would never have thought of that. I tend to think of logs as mysterious values with no intuitive interpretation.
Hi Suzanna, Roland from Venray, NL here. I've seen some of your video's the last couple of days. Before I saw comparable videos of, primarily (BTW brilliant) Indian guys, but, although the steps they followed were correct, I missed the 'whys' and 'whens', whereas you explain in an almost childish manner (not an offence; a compliment!!!) how to solve such problems. Chapeau! (If you're not familiar with French: Hats off!)
Hi Roland, thank you so much for your kind words! We actually learn French at school in Germany and this is me 11 years ago: ua-cam.com/video/XqBy8ftwCcM/v-deo.htmlsi=nD-yVSsAC6iEv5ou
@MathQueenSusanne Also kann ich auch auf Deutsch mit dir reden. Werde ich aber nicht mehr tun, weil viele anderen Leute es nicht verstehen würden. Übrigens: Schone stimme und auch noch piano-fähig! Großartig!
*Stimme
My math book said: log (2) 16 = 4 because 16 = 2 raised to the 4th power. That was it, no further explanation. I have an easy time understanding math, but I have an even easier time with your explanation.
Thanks. A good refresher for me.
0:50 'How often have we multiplied the four by itself?' The answer is one time.
Should say how many terms in the multiplication
Only if you're being overly pedentic.
@toby9999 yeah, maths is no place for accuracy!
She is the Algebra teacher from our dreams.
danke, susanne, klasse erklärt
2^x = 1/8
2^x = 2^-3 change bases to same value
x = -3 the only difference is now in the exponents
I needed this.
Reminds me of my favorite math teacher...
While I LOVE your videos, I must admit, everything after "Hello my lovelies" was WAAYYYY above my paygrade ;-)
Although I do hope something you said will creep into my feeble mind!!!
I think changing from logarithmic to exponential form could have been a better approach.
log1/6(36)=x
36= (1/6)^x
6^2= 6^-x
2=-x
x=-2
Thank you very much, I really suffered at the hands of logs😂its payback time🎉
I like being referred to as "lovely". Doing math is the bonus.
Click like if you’ve ever had to use this type of math in your life so far apart from school lessons .
Every Damn Day. Such is the life of a data architect
Yup, data analyst here
@wheechie Microslop didn't make it any easier with their choice of integer basis for universe date either. Who da phuq has 1900-01-01 at midnight as their universe date?
Thanks that was great
Great explanation
That was awsome!
Thanks for that. I did not know these shortcuts. 👍🏿
Dankeschoen! Ich mag math.
Very interesting video 😊
Thanks. How about for the numbers that don't multiply into the numbers. Let us say log(9) or log(27) or log3(10)? Is there a way?
Nice video and great examples increasing in difficulty, but i was waiting for when the answer didn't round out so nicely. It didnt come. For example, what if the last one was Log 2/3 of 16/80?
For the cases where you had a log of 1/n that is the same as n to the power of -1. You move the -1 to the front then you have negative log of n. It skips that expansion you did where you wind up with a term of 0. You can use that same identity when dealing with a fractional base. EDIT: The other way to do logs without a calculator is to use a slide rule. :)
So how about log3(4) or log7(11)? And loge(10), where e=sum(1/n) n=1 -> infinity
The reason any base to the power of zero is one which means log 1 = 0 for any base, can be shown like this.
Division requires exponents be subtracted.
n^x/n^x = 1
n^x/n^x = n^(x-x) = n^0
So, n^0 = 1
It is a provable fact and does not rely on the old, "we define it that way.
How about when n=0? I think this is a strange one, right?
You say "we have to count how often we have mutiplied ..." but the relevant number here is not the number of multiplications but the number of factors, which is the number of multiplications plus one.
Exactly! I noticed this as well. While the intention of that phrase was fairly clear, I think the wording could’ve been more precise.
I had a "nightmare" teacher who would make up the test questions, off the top of his head, at the beginning of class. You might get craziness like, log 0.003 or log 11. The book had nice, neat answers, like yours. His could be some horrifying fraction, or even no solution, at all. A couple of times, even he said, "Ooh, this was a bad question," as he struggled to solve it. His motto was: Use your tools; Work the problem.
I drop logs 🪵 in the pan usually 3 logs a day x 16 sheets to wipe my bottom how many sheets where logged out
Suzanna, please do more logarithms.
What do we do when the numbers are not so nice, such as log (base 10) 1100
If'ns I was to guess, I'd say we factor the 1100 into 1000 * 1.1 so log(1000)+log(1.1), then treat log(1.1) as log(11/10) ? But with the method shown, log(11/10) = log(1)...
In programming, logs without base always mean base 2 due to the binary nature of computer architecture.
With base 10 all you have to remember is log(2)=~0.3, log(3)=~0.48 and log(7)~=0.85. All the others are either trivial or combinations of those 3:
log(1) = 0, easy to remember as is log(10) = 1
log(4) = log(2 * 2) = 0.3 + 0.3 = 0.6
log(5) = log(10 / 2) = 1 - 0.3 = 0.7
log(6) = log(2 * 3) = 0.3 + 0.48 = 0.78
log(8) = log(2 * 2 * 2) = 0.3 + 0.3 + 0.3 = 0.9
log(9) = log(3 * 3) = 0.48 * 0.48 = 0.96
With that you can raise any number to any power (or find any root of any number) with surprising accuracy by reducing the number to the 0-1 range (keeping the exponent in mind), using basic linear interpolation between the known values in that range to get the log of your base, dividing or multiplying by the power/index and then repeating the process in reverse to find the inverse log, which in turn gives you your final answer. Requires a bit of practice, but can certainly be done in your head if you have some basic math skills.
That blows my mind... really?
It seems to work, but I can feel my brain exploding. It's baffling how that can work.
4:44 this is probably a stupid question but instead of moving the power of 2 to the front of the Log why not just operate 27^2 and then resolve the logarithm
You could, but that is usually harder than just multiplying by the exponent.
hhhhhhhhh
good method
and here is another method
log ( 2/3 ; 16/81) = log( 16/81) / log (2/3) = log ( 2^4 /3^4) /log( 2/3)
= log ((2/3)^4)) / log(2/3 ) = (4 log(2/3)) / log(2/3) = 4
ps : c'est une très bonne méthode pour expliquer le calcul des logarithmes
mais il ne faut pas oublier que seuls 3 logarithmes sont les plus utilisés
1- log (10 ; x ) = log x .........( la notation admise
2- log ( e ; x ) = Ln x = Log x ........( la notation admise
3- log (2 ; x ) = log (2 ; x) .........( la notation admise
I like how you teach
Thanks!
In some contexts they write log when they mean ln. Its use is deprecated by ISO, but who listens to them?