Question

Simplify ${\log }_{\sqrt{2}}256$.

Answer 1

${\log }_{\sqrt{2}}256=\frac{{\log }_{10}256}{{\log }_{10}\sqrt{2}}$ $(\because {\log }_{a}b=\frac{{\log }_{10}a}{{\log }_{10}b})$

$=\frac{\log 2^8}{\log 2^{\frac{1}{2}}}=16$