Question

What is the value of ${\log }_{8}512$?

Answer 1

Find the value of ${\log }_{8}512$.

$\begin{array}{rcl}{\log }_{8}512& =& {\log }_8{8}^3\\ & =& 3{\log }_{8}8\\ & =& 3\left(1\right)\left\{\because {\log }_{a}a=1\right\}\\ & =& 3\end{array}$

Hence, the value of $\begin{array}{l}{\log }_{8}512\end{array}$ is $3$.