Answer
$x = -\dfrac{\ln{1.5}}{\ln{2}} \approx -0.585$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{(2^{-x})} = \ln{1.5}$
Use the rule $\ln{a^x} = x \cdot \ln{a}$ to obtain:
$-x\cdot \ln{2} = \ln{1.5}$
Divide both sides of the equation by $-\ln{2}$ to obtain:
$\dfrac{-x\cdot \ln{2}}{-\ln{2}}=\dfrac{\ln{1.5}}{-\ln{2}}
\\x = -\dfrac{\ln{1.5}}{\ln{2}}
\\x \approx -0.585$
