Answer
$x = 5$
Work Step by Step
Write $243$ as $3^5$:
$3^{-x} = \dfrac{1}{3^5}$
Use the rule $\frac{1}{a^m}=a^{-m}$:
$3^{-x} = 3^{-5}$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$:
$-x = -5$
Divide both sides by $-1$ to solve for $x$:
$x = 5$
