1.[latex]log_{2} \sqrt{ \frac{1}{8} } [/latex] 2.[latex]log_{\sqrt{2}} \frac{\sqrt{2}}{2} }[/latex]

1) [latex]log_{2} \sqrt{ \frac{1}{8} } =log_{2} ( \frac{1}{8} } )^{ \frac{1}{2} } =log_{2} ( 2^{-3} } )^{ \frac{1}{2} }=- \frac{3}{2}=-1.5 [/latex] 2) [latex]log_{\sqrt{2}} \frac{\sqrt{2}}{2} }=log_{\sqrt{2}} \sqrt{ \frac{2}{4} } =log_{\sqrt{2}} \sqrt{ \frac{1}{2} } =log_{ 2^{0.5} } ( \frac{1}{2} }) ^{0.5} =0.5*2log_{ 2 } \frac{1}{2} }=[/latex][latex]=log_{ 2 } 2^{-1} =-1[/latex]