Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 100

$-\dfrac{\ln{\left(\dfrac{1}{3}\right)}}{2}$

$\because e^y=x \text{ is equivalent to } y=\ln{x}$ $\therefore e^{-2x} = \dfrac{1}{3} \text{ is equivalent to } -2x=\ln{\left(\dfrac{1}{3}\right)}$ Solve the equation above to obtain" \begin{align*} -2x&=\ln{\left(\dfrac{1}{3}\right)}\\\\ x&= -\dfrac{\ln{\left(\dfrac{1}{3}\right)}}{2} \end{align*}