Answer
$x =-\dfrac{\ln{(\frac{1}{3})}}{2}$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{e^{-2x}} = \ln{(\frac{1}{3})}$
RECALL:
$\ln{e^a} = a$
Use the rule above to obtain:
$-2x=\ln{(\frac{1}{3})}$
Divide by $-2$ on both sides of the equation to obtain:
$x =\dfrac{\ln{(\frac{1}{3})}}{-2}
\\x =-\dfrac{\ln{(\frac{1}{3})}}{2}$
