Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 66

$x=-4$

Since $81=3^4$, then $3^{-x}=3^4$. The base is the same on the 2 sides of the equation (and it is not 1), hence they will be equal if the exponents are equal. Thus, \begin{align*} -x&=4 \\x(-1)&=4(-1)\\ x&=-4\end{align*}