Answer
$e$
Work Step by Step
Let $
x=10^{\log e}
$. Taking the logarithm of both sides results to
\begin{align*}\require{cancel}
\log x&=\log10^{\log e}
.\end{align*}
Using the properties of logarithms, the equation above is equivalent to
\begin{align*}\require{cancel}
\log x&=(\log e)(\log10)
&(\text{use }\log_b x^y=y\log_b x)
\\
\log x&=(\log e)(1)
&(\text{use }\log 10=\log_{10}10=1)
\\
\log x&=\log e
.\end{align*}
Since $\log x=\log y$ implies $x=y$, then the equation above implies
\begin{align*}
x&=e
.\end{align*}
With $x=10^{\log e}$ and $x=e$, then $
10^{\log e}
$ evaluates to $
e
$.
