Question

$log0.5 \sqrt{2}$

Answer 1

$log_ \frac{1}{2} \sqrt{2}=k \\ \sqrt{2}=( \frac{1}{2})^k \\ 2^( \frac{1}{2})=(2^{-1})^k \\ 2^{ \frac{1}{2}}=2^{-k} \\ -k= \frac{1}{2} \\ k=- \frac{1}{2} \\ log_{ \frac{1}{2}} \sqrt{2} =- \frac{1}{2}$