Chapter 4 - Exponential and Logarithmic Functions - Section 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 94

$-4$

$\because y = \ln{x} \text{ is equivalent to } x=e^y$ $\therefore 8= \ln{e^{-2x}} \text{ is equivalent to } e^{-2x}=e^8$ Solve the equation above using the rule $a^m=a^n \implies m=n$ to obtain: \begin{align*} e^{-2x}&=e^8\\\\ -2x&=8\\\\ \frac{-2x}{-2}&=\frac{8}{-2}\\\\ x&=-4 \end{align*}