Answer
$a.\qquad \sqrt{3}$
$b.\qquad 4$
$c.\qquad 13$
Work Step by Step
By definition, $\log_{a}x=y \Leftrightarrow a^{y}=x$
($\log_{a}x$ is the exponent to which the base $a$ must be raised to give $x$.)
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What follows from the definition is that
$\log_{a}(a^{x})=x$ and $a^{\log_{a}(x)}=x$
"ln" is special annotation for the natural logarithm, $\log_{e}$ (with base e).
"log" (without a base) stands for $\log_{10}$, the common logarithm.
a.
$e^{\ln\sqrt{3}}=e^{\log_{e}(\sqrt{3})}=\sqrt{3}$
b.
$\ln e^{4}=\log_{e}e^{4}=4$
c.
$10^{\log 13}=10^{\log_{10}(13)}=13$
