Solve for x:

Question

2^(-x+1) = 4(8^x)

I try isolating the 4 but I can't seem to solve it correctly when using ln or log applications. The answer is supposed to be x=-1/4. Any help?

Answer 1

first, express 4 as a power of 2,,
4=2^2
then divide both sides by 2^2
2^(-x+1)/2^2 = 8^x
*note, at the right side of equation, 4 and 2^2 canceled each other*
then recall some laws of exponents. since on the left side, the numerator and denominator have the same base (which is 2), we can combine their exponents:
2^(-x+1-2)=8^x
express 8 as a power of 2:
2^(-x-1)=2^(3x)
equating the exponents:
-x-1=3x
4x=-1
x=-1/4

so there, i hope i was able to help.. =)