8^(2/3)·8^(3/4) = 8^(2/3 + 3/4) = 8^(8/12 + 9/12) = 8^(17/12) = [2^(3)]^(17/12) = 2^(3·17/12) = 2^(17/4). Now compare 2^(17/4) = 2^(x/4) => x = 17. But this is only the solution in ℝ.
Algebruary Calendar Day 10 : 1/23*(3^(2-sqrt(5)))^(2+sqrt(5))=1/23*exp((2+sqrt(5))*ln(3^(2-sqrt(5)))) =1/23*exp((2+sqrt(5))*(2-sqrt(5))*ln(3)) =1/23*exp((2^2-(sqrt(5))^2)*ln(3)) =1/23*exp((4-5)*ln(3)) =1/23*exp(-ln(3)) =1/(23*exp(ln(3))) =1/(23*3) =1/69 answer : 1/69 Algebruary Calendar Day 11 : Study of function : f(x)=x^(1/x) (for any x>0) f(x)=exp(ln(x)/x) (f(x)>0 for any x>0) df(x)/dx=f'(x)=f(x)*(1/x*x-ln(x)*1)/x^2=f(x)*(1-ln(x))/x^2 f(x) has the same sign that (1-ln(x)) If 0exp(1) then ln(x)>1 then (1-ln(x))
Got I before he did. And I had the video on 2x. 8^(2/3)*8^(3/4)=2^(x/4) 8^(2/3+3/4)=2^(x/4) 8^(17/12)=2^(x/4) (2^3)^(17/12)=2^(x/4) 2^(17/4)=2^(x/4) 17/4=x/4 x=17 (I don’t know how to put a box around it)
Algebruary Calendar Day 2 : 8^2/3*8^3/4=8^(2/3+3/4)=8^(8/12+9/12)=8^(17/12)=(2^3)^(17/12)=2^(3*17/12)=2^(17/4) answer : x=4 Algebruary Calendar Day 3 : (2^x+2^y)^2=6^2=36 (2^x)^2+(2^y)^2+2*2^x*2^y=36 4^x+4^y+2*2^(x+y)=36 4^x+4^y+2*2^2=36 4^x+4^y=36-8=28 answer : 28 Algebruary Calendar Day 4 : Method 1 : i use a calculator : 2^sqrt(3)=3,32 on average and 3^sqrt(2)=4,73 on average answer : 3^sqrt(2) larger than 2^sqrt(3) Method 2 : we will proof that 2^sqrt(3)
Andy uploading on my birthday 🥳🫅🏾🎗️🎉
Happy Birthday!
@@AndyMath Thank you so much!
Happy Birthday man!
@@Joshua45489 Thank you bro 👑
boobs, 69 and 420 all in the same math problem!? top tier math problem
I knew he'd do that to us!! Lol
Don't forget "four-hunnit" 1:40. My man hit the trifecta with flare points on top!
@@Drip_Dry i missed that!
And 80085!
@KinLeung-gm6mr that's boobs
First I was like "nice", then I was like "nice" and in the end I was like "nice"
My goal: learn to pronounce Algebruary by Feb 28
/aldʒebɻuaɹi/
It's like algrebra + ferrari (alge+rrari) but whit a b
use ipa
Finally something I can actually do without finding similar triangles! LOLOL - Thank you for doing these!
You're doing another entire month!? I am so here for it!
Lol 69 and 420 in same video😂
Also 80085 - aka boobs
and 80085
Not to mention 80085
My thoughts exactly, first time 'This looks like a fun one' was a legit statement :)
I predict Andy will be done somewhere around March 4
80085 - nice 😎
69 - nice 😎
fo' hunnid - nice 😎
420 - nice 😎
Great way to start the month lmao at those meme numbers
How exciting. Will be interesting to see if you stumble this month too.
I am so happy with the calendars ❤ how exciting!
So much swag in one equation. Starting off Algebruary with a bang.
Glad to see you're back. After all the trig in December you needed some time off I guess. 😁👍
Walter white, let's cook some math
Next series idea: Calcu-lent
Happy new year, Andy!
I'm guessing half of the month's answers will be either 69 or 420.
8^(2/3)·8^(3/4) = 8^(2/3 + 3/4) = 8^(8/12 + 9/12) = 8^(17/12) = [2^(3)]^(17/12) = 2^(3·17/12) = 2^(17/4).
Now compare 2^(17/4) = 2^(x/4) => x = 17. But this is only the solution in ℝ.
Oh, I did it with logarithmic transformation! Same answer, cool.
Day 1 and all I can think of is whether he will finish on time. Go Andy Go!
what a great concept!
Andy: the man behind my passion for math
As a saucy hippy, I appreciate these numbers...
Peace all xx
80085, 420, and 69 in one equation? That's no accident lol
Fireee🔥🔥🔥
Easy problem for tomorrow. Finished it in my head before the video ended.
80085 every boy starts laughing and girls don’t know why.
This is a short month, so any late submissions will lose 10% per day. Good luck Andy!
Bravo, sir 🫡
Nice!
Nice, nice, and nice.
i wonder how many extra day of enjoymant we get this time as it slip over in to march. epic solve as alwsy.
I'll celebrate your answer with some California produce.
Bro teach us make a full length video covering different topics of math it will be very helpful for many people.
ZOMG! The geometric ones (December?) were enlivening, but this is just like punishing HS homework. Too late to re-cast February as something else?
What happened to January?
Algebruary Calendar Day 10 :
1/23*(3^(2-sqrt(5)))^(2+sqrt(5))=1/23*exp((2+sqrt(5))*ln(3^(2-sqrt(5))))
=1/23*exp((2+sqrt(5))*(2-sqrt(5))*ln(3))
=1/23*exp((2^2-(sqrt(5))^2)*ln(3))
=1/23*exp((4-5)*ln(3))
=1/23*exp(-ln(3))
=1/(23*exp(ln(3)))
=1/(23*3)
=1/69
answer : 1/69
Algebruary Calendar Day 11 :
Study of function : f(x)=x^(1/x) (for any x>0)
f(x)=exp(ln(x)/x) (f(x)>0 for any x>0)
df(x)/dx=f'(x)=f(x)*(1/x*x-ln(x)*1)/x^2=f(x)*(1-ln(x))/x^2
f(x) has the same sign that (1-ln(x))
If 0exp(1) then ln(x)>1 then (1-ln(x))
get meme'd on
This is a little more my speed lol
8^(2/3) * 8^(3/4) = 2^(x/4)
{a^b * a^c = a^(b+c)}
8^(2/3 + 3/4)=2^(x/4)
8^(17/12)=2^(x/4)
{8= 2^3}
2^(3 * 17/12) = 2^(x/4)
2^(51/12)=2^(x/4)
{51/12=17/4}
2^(17/4)=2^(x/4)
x=17
this math problem is so whimsy and childish I love it tbh
Algebruary Calendar Day 5 :
3^x+3^(x+1)+3^(x+3)=31/3
3^x+3^x*3^1+3^x*3^3=31/3
3^x+3*3^x+27*3^x=31/3
(1+3+27)*3^x=31/3
31*3^x=31/3
3^x=1/3
ln(3^x)=ln(1/3)
x*ln(3)=-ln(3)
answer : x=-1
Algebruary Calendar Day 6 :
5^(x+2)=71+5^x+5^2=71+5^x+25=5^x+96
5^x*5^2=25*5^x=5^x+96
(25-1)*5^x=96
24*5^x=96
5^x=96/24=4
answer : 5^x=4
Algebruary Calendar Day 7 :
(7*x)^(1/3)=x^(1/2) (with x>0)
((7*x)^(1/3))^6=(x^(1/2))^6
(7*x)^2=x^3
49*x^2=x^3
49*x^2-x^3=0
x^2*(49-x)=0
49-x=0
answer : x=49
Algebruary Calendar Day 8 :
I don't know today how to solve this exercise : i must look up "Power Towers"
Algebruary Calendar Day 9 :
3^(x^(1/3)+3)=1^(sqrt(-2*x)+x)
1^(sqrt(-2*x)+x)=1 for any x negative or equal to 0 (necessary condition because "sqrt" then "-2*x>0")
3^(x^(1/3)+3)=1
ln(3^(x^(1/3)+3))=ln(1)=0
(x^(1/3)+3)*ln(3)=0
x^(1/3)+3=0
x^(1/3)=-3
(x^(1/3))^3=(-3)^3=-3^3=-27
x=-27
answer : x=-27
Algebruary Calendar Day 14 :
x^5+x^5+x^5=3^11
3*x^5=3*3^10
x^5=3^10=(3^2)^5=9^5
f(x)=x^5 is a monotically increasing function then : x=9
answer : x=9
Algebruary Calendar Day 15 :
(27/8)^x=32/243
(3^3/2^3)^x=2^5/3^5
((3/2)^3)^x=(2/3)^5
(3/2)^(3*x)*(3/2)^5=1
(3/2)^(3*x+5)=1
ln((3/2)^(3*x+5))=ln(1)=0
(3*x+5)*ln(3/2)=0
3*x+5=0
answer : x=-5/3
Algebruary Calendar Day 16 :
-2*(-2^2+2^(-2))^(-2)=-2*(-4+1/2^2)^(-2)=-2*(-4+1/4)^(-2)=-2*(-15/4)^(-2)=-2*(-4/15)^2=-2*16/225=-32/225
answer : -32/225
I can't show these in my class because of the fun numbers 😩
Nice
Got I before he did. And I had the video on 2x.
8^(2/3)*8^(3/4)=2^(x/4)
8^(2/3+3/4)=2^(x/4)
8^(17/12)=2^(x/4)
(2^3)^(17/12)=2^(x/4)
2^(17/4)=2^(x/4)
17/4=x/4
x=17 (I don’t know how to put a box around it)
|--------|
|x=17|
|--------|
I am typing my answer for tomorrow's right here
x = 17
Anyhow - I can see some improvement to the vocabulary
I miss Catriona Agg.
4 hunnit 😂😂😂
... nice.
Algebruary Calendar Day 2 :
8^2/3*8^3/4=8^(2/3+3/4)=8^(8/12+9/12)=8^(17/12)=(2^3)^(17/12)=2^(3*17/12)=2^(17/4)
answer : x=4
Algebruary Calendar Day 3 :
(2^x+2^y)^2=6^2=36
(2^x)^2+(2^y)^2+2*2^x*2^y=36
4^x+4^y+2*2^(x+y)=36
4^x+4^y+2*2^2=36
4^x+4^y=36-8=28
answer : 28
Algebruary Calendar Day 4 :
Method 1 : i use a calculator :
2^sqrt(3)=3,32 on average and 3^sqrt(2)=4,73 on average
answer : 3^sqrt(2) larger than 2^sqrt(3)
Method 2 : we will proof that 2^sqrt(3)
Day 2, x = 17
Day 2 answer - x=17
8^(2/3+3/4)=8^(x/12)
2/3+3/4=x/12
8/12+9/12=x/12
9+8=x
X=17
Hunnit
I used to say Febuary.
When is this kind of math ever useful in the real world?
Day 2 x= 17
Is he using 69 and 420 in his problems on purpose? It’s not the first time lol
420!
Day 2 x is 17
Day 3 The answer is 28
Day 4. 3^(✓2)
Day 5 x=(-1)
Day 6 5^(x)=4
Day7 x=49
Spoiler, feb 2's answer is 17, imo
Jolly joker! Are you and Elon Musk fan?😅
know the answer from the thumbnail. lol
17
Impossible.
x=17
i mean it's very "nice"
Math nerds need to figure out some new jokes.
Oh god not algebra
λ^2=sqr((x=sqr(420)-yspr(69))-20)
Not good at mathround 🎉
Very nice
Bro this is so easy i can just Do whatever i want to cancel 2 numbers and easy lol
we do not call it "difficult" when there is just a larger numbers!!!
I believe you missed the joke(s). Maybe faith has made you blind...
do you mean 69 and 420? btw i have nothing related with the word of "faith", my name is Fatih, i believe you screwed the humour 😅
Nice