Question

1.$log_{2} sqrt{ frac{1}{8} }$
2.$log_{sqrt{2}} frac{sqrt{2}}{2} }$

Answer 1

1)
$log_{2} sqrt{ frac{1}{8} } =log_{2} ( frac{1}{8} } )^{ frac{1}{2} } =log_{2} ( 2^{-3} } )^{ frac{1}{2} }=- frac{3}{2}=-1.5$

2)
$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} }=$$=log_{ 2 } 2^{-1} =-1$