Answer
$\displaystyle \frac{1}{2}$
Work Step by Step
$10^{2}=100\quad\Rightarrow\quad 10=100^{1/2}$
$\log_{100}(10)=\log_{100}(100^{1/2})\quad$... Apply the property $\log_{a}a^{k}=k$
$=\displaystyle \frac{1}{2}$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.