Question

Solve the following inequality:
${\log }_2(2x-1)>{\log }_{1/\sqrt{2}}2$

Answer 1

${\log }_2(2x-1)>-\frac{\log 2}{\frac{1}{2}\log 2}{\log }_2(2x-1)>-22x-1>2^{-2}2x>1+\frac{1}{4}x>\frac{1}{2}+\frac{1}{8}x>\frac{5}{8}x\in (\frac{5}{8},\infty )$ and $2x-1>0x>\frac{1}{2}x\in (\frac{1}{2},\infty )$

Taking intersection, we get $x\in (\frac{5}{8},\infty )$