Question

Solve:

${\log }_{\sqrt{2}}512$

Answer 1

${\log }_{\sqrt{2}}512=\frac{{\log }_{10}512}{{\log }_{10}\sqrt{2}}=\frac{{\log }_{10}{2}^9}{\frac{1}{2}{\log }_{10}2}=\frac{9\times 2{\log }_{10}2}{{\log }_{10}2}=18$