Answer
$f^{-1}(x) = \log_7 x$
Work Step by Step
$f(x) = 7^{x}$
Let $f(x) = y$
$y = 7^{x}$
Swap the $x$ and $y$ variable then solve for $y$ to find the inverse:
$x = 7^{y}$
$y = \log_7 x$
$f^{-1}(x) = \log_7 x.$
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