AoPS Wiki talk:Problem of the Day/June 13, 2011

Problem

This Problem of the Day needs a solution. If you have a solution for it, please help us out by adding it.

First, we can simplify the fraction on the right side of the equation by subtracting the exponents of both numbers.

${\dfrac{2^{3x+7}}{2^{x-1}}=2^{(3x+7)-(x-1)}=2^{2x+8}$ (Error compiling LaTeX. Unknown error_msg)

$8=2^3$ Thus, we add 3 to the exponent.

$2^{x+5}=2^{2x+11}$

Then, we can divide both sides by the left side.

$1=2^{(2x+11)-(x+5)}=2^{x+6}$

$1=2^0$ Therefore,

$0=x+6$

$x=\boxed{-6}$