Answer
$x=-\displaystyle \frac{1}{2}\log_{3}4$
Work Step by Step
The base $b$ logarithm of $x,\log_{b}x,$
is the power to which we need to raise $b$ in order to get $x$ .
Symbolically, $\quad \log_{b}x=y\quad $ means $\quad b^{y}=x$
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$3^{-2x}=4\quad $ means $\quad -2x=\log_{3}4,$
... divide the last equation by $(-2)$
$x=-\displaystyle \frac{1}{2}\log_{3}4$
