Answer
$a.\qquad 5$
$b.\qquad 27$
$c.\qquad 10$
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 $x$.)
---
What the definition states is that$ \log_{a}(x)$ and $a^{y}$ are inverse functions,
$\log_{a}(a^{x})=x$ 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.
$3^{\log_{3}5}=5$
b.
$5^{\log_{5}27}=27$
c.
$e^{\ln 10}=e^{\log_{e}(10)}=10$
