Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 64

$x=-4$

Re-write the given equation as: $3^{-x}=3^4$ $(Because: \ 81=3^4)$ Use the rule power rule: $a^p=a^q$ . We can see that the base $a=3$ is the same on both sides of the equation. So, the exponents will also be equal. This implies that $p=q$ Therefore, $3^{-x}=3^{4} \implies x=-4$