Question

Find the value of ${\log }_{\sqrt{2}}64.$

Answer 1

Let $a={\log }_{\sqrt{2}}64$

$a={\log }_{2^{\frac{1}{2}}}{2}^6$

Using ${\log }_{b^n}{a}^m=\frac{m}{n}{\log }_{b}a$

$a=\frac{6}{\left(\frac{1}{2}\right)}{\log }_{2}2$

Since ${\log }_{a}a=1$

$a=6\times 2=12$