Yes, true. But you also have to observe that 4^x - 2^x - 12 is ever increasing, as x increases, so there is at most one solution to 4^x - 2^x - 12 = 0 and you found it.
Yes just use substitution. y²-y-12=0 . Then just solve the quadratic equation and equate 2^x to be the the solution of that equation and then solve it using logarithms and then use your calculator
@@rivenoak I solved it differently: since after making 4^x of the base 2, the powers can be added. So, I added power of x to 2. Then I got 2^(2+x) and moved -12 to the other side which became +12. Then I took logs of every expression and also the solution was +2.
@@user-ky5dy5hl4d perhaps the equation was a question in another vid already or it was a tickle in my brain which loves math problems: the solution poked me very soon. no log calculations required, but it wont work every time for sure
@@rivenoak If you love math problems then I do, too. But I also love physics problems. Maybe you can help me. What causes the speed of light? What is the definition of time?
I agree that you should always check your candidate solutions to see if they are correct. In this case, it's quite simple to do this, 4ˣ-2ˣ-12=4²-2²-12=16-4-12=0 so it is a good solution.
If x E R we can use also this method: 4^x - 2^x - 12 = 0 2^(2)x - 2^x = 12 2^(2x) - 2^x = 16 - 4 2^(2x) - 2^x = 2^4 - 2^2 (the same bases and the same operation, we can compare all exponents of LHS and RHS) 2x = 4 and x = 2 x = 2
@@ccboys3430 Correct. That is why you can move -12 on the other side od the equation and have +12. Also, there is a difference between -log(x) and -log(-x) or log(-x). In negative x you can't use negative numbers. But -log(x), one can.
If i said it once, I've said it hundred times, THANK YOU. only one thing, i don't think they teach this to 9 or 10 graders in this country, maybe 2nd year in college. 😂😂😂
Giving me every desire to go back and revisit those maths classes from 26 years ago. You bring so much understanding to the topic. Thank you.
My math teacher said that substitution is the makeup of maths which makes math look beautiful 😂🤯
The method of substitution stays forever important in the field of mathematic calculations. Thank you very much, Sir.
Just looking at the equation I thought that x was 2.
Yeah me too, 😂😂😂
Thank you sir.
Great class
I want to see the complex solution.
I love this type of problem because I can just do it in my head especially when I got lazy to grab a pen and paper lol
❤❤
(4x4)-(2x2)-12 is the aswer
Math has a different symbol/statement for no solutions. Part of void, no equal
Just looking at this and without even having watched the video, I immediately see that x = 2.
Yes, true. But you also have to observe that 4^x - 2^x - 12 is ever increasing, as x increases, so there is at most one solution to 4^x - 2^x - 12 = 0 and you found it.
relatable
Yes just use substitution. y²-y-12=0 . Then just solve the quadratic equation and equate 2^x to be the the solution of that equation and then solve it using logarithms and then use your calculator
So basically the problem is complex because we dont know the x and so on
2^2x-2^x-12=0
2^x=y
y^2-y-12=0
y=[1+-rq(1+48)]/2
y=[1+-7]/2
y1=4 y2=-3
Anyone interested in how to handle the complex case?
personally id log the equation
16-4=12 is obvious here
@@rivenoak I solved it differently: since after making 4^x of the base 2, the powers can be added. So, I added power of x to 2. Then I got 2^(2+x) and moved -12 to the other side which became +12. Then I took logs of every expression and also the solution was +2.
@@user-ky5dy5hl4d perhaps the equation was a question in another vid already or it was a tickle in my brain which loves math problems: the solution poked me very soon.
no log calculations required, but it wont work every time for sure
@@rivenoak If you love math problems then I do, too. But I also love physics problems. Maybe you can help me. What causes the speed of light? What is the definition of time?
Can't add the powers @@user-ky5dy5hl4d
Nose bleeding again😳
Stop picking your nose. Its symbolic of schizophrenia.
You should include the proof of you answer. Show how you can plug your solution back into the original equation.
I agree that you should always check your candidate solutions to see if they are correct. In this case, it's quite simple to do this, 4ˣ-2ˣ-12=4²-2²-12=16-4-12=0 so it is a good solution.
Why doesn't the following have the same result?
x log(4) - x log(2) = log(12)
log(a+b)≠log(a)+log(b), only
log(ab)=log(a)+log(b)
@@lifewatery7472 ohhhhhhhh! Thanks!
X=2.
4^x-2^x-12=0
(2^x)²-2^x-12=0
Let y=2^x
y²-y-12=0
(y+3)(y-4)=0
y+3=0
y=-3
2^x=-3 (not possible)
y-4=0
y=4
2^x=2²
x=2 ❤
If x E R we can use also this method:
4^x - 2^x - 12 = 0
2^(2)x - 2^x = 12
2^(2x) - 2^x = 16 - 4
2^(2x) - 2^x = 2^4 - 2^2 (the same bases and the same operation, we can compare all exponents of LHS and RHS)
2x = 4 and x = 2
x = 2
It may be obvious that the solution is +4. But one can use log, too.
Log doesn't allowed negative number 😅
@@ccboys3430 Correct. That is why you can move -12 on the other side od the equation and have +12. Also, there is a difference between -log(x) and -log(-x) or log(-x). In negative x you can't use negative numbers. But -log(x), one can.
@@user-ky5dy5hl4dlog(-x) is possible
Just by looking at the problem, I had the answer..
this was so easy
X=0
If i said it once, I've said it hundred times, THANK YOU.
only one thing, i don't think they teach this to 9 or 10 graders in this country, maybe 2nd year in college. 😂😂😂