Question

Find the exact solution to the equation. Show your work.

4^(12-4x) = 256
(I know the answer is 2, the thing I don't know how to do correctly is showing my work)

Answer 1

Hi

4^(12-4x) =256
First we need to take log of both sides
log(4^-4x+12) = log (256)
(-4x + 12)(log(4)) = log(256)
so now we have
-4x + 12 = log(256)/log(4)
-4x + 12 = 4
-4x = 4 - 12
-4x = -8
x = -8/-4
x= 2

I hope that's help :)

Answer 2

Hello,


`4^(12-4x)=256\\ ==\ \textgreater \ \ 2^(24-8x)=2^8\\ ==\ \textgreater \ \ 24-8x=8\\ ==\ \textgreater \ 8x=16\\ ==\ \textgreater \ x=2`