Answer
$y=\frac{1}{10} \cdot 10^x$ or $y=10^{x-1}$
Work Step by Step
To find the inverse of the given function, perform the following steps:
(1) Interchange $x$ and $y$:
$$x=\log{10y}$$
(2) Write the equation in exponential form using the definition $y=\log_a{x} \longleftrightarrow a^y=x$:
$$10^x=10y$$
(3) Solve for $y$:
\begin{align*}
10^x&=10y\\\\
\frac{10^x}{10}&=y\\\\
y&=\frac{1}{10} \cdot 10^x\end{align*}
Note that $\dfrac{10^x}{10}=10^{x-1}$.
Thus, the inverse of the given function is:
$y=\frac{1}{10} \cdot 10^x$ or $y=10^{x-1}$