1 . Oblicz. a) log ₀,₅16 b) log₂[latex] frac{1}{ sqrt{2} } [/latex] 2. Znajdz x : a) log₀,₅x=-5 b) logₓ0,25=0,5

[latex]1. \ log_{0,5}16= log_{ frac{1}{2}}2^{4}=log_{2^{-1}}2^{4}=x \ -x=4 \ x=-4 \ \ log_{2} frac{1}{ sqrt{2} } = log_{2}2^{- frac{1}{2} }=x \ x=- frac{1}{2} \ \ \ 2. \ log_{0,5}x=5 \ log_{2^{-1}}x=5 \ (2^{-1})^{5}=x\x=2^{-5}\x= frac{1}{32} \ \ log_{x} frac{1}{4}= frac{1}{2}\x^{ frac{1}{2}}= frac{1}{4}\ sqrt{x}= frac{1}{4}\x= frac{1}{16} [/latex]