Answer
$\dfrac{1}{2}$
Work Step by Step
Note that $10=\sqrt{100}$.
Replace $10$ with its equivalent of $\sqrt{100}$ to obtain:
$=\log_{100}{(\sqrt{100})}$
Use the rule $\sqrt{a}= a^{\frac{1}{2}}$ to obtain:
$=\log_{100}{(100^{\frac{1}{2}})}$
RECALL:
$\log_b{b^x} = x$
Use the rule above to obtain:
$=\dfrac{1}{2}$
