Answer
$x=-\dfrac{\ln{1.5}}{\ln{2}}\approx -0.585$
Work Step by Step
Take the $\log_2$ of both sides:
$\log_2{2^{-x}}=\log_2{1.5}\\-x=\log_2{1.5}$
Multiply $-1$ to both sides to obtain:
$x=-\log_2{1.5}.$
We know that $\log_a {b}=\dfrac{\log_c {b}}{\log_c {a}}$ (Change of Base Formula).
Hence, using the change-of-base formula and a calculator gives
$x=-\log_2{1.5}=-\dfrac{\ln{1.5}}{\ln{2}}\approx-0.585$
