1. Oblicz: 1) [latex] log_{ sqrt{2} } 2 sqrt{2} [/latex] 2. Oblicz podstawę logarytmu:  1) [latex]log_{a}2 = frac{1}{2} [/latex] 2) [latex] log_{a}8=6 [/latex] 3)[latex] log_{a}32=-5 [/latex] Proszę o pomoc :P

def logarytmu [latex]log_ab=c -> a^c=b[/latex] 1. [latex]log_ {sqrt{2}} 2 sqrt{2} =x\ sqrt{2}^x= 2 sqrt{2}\ (2^{ frac{1}{2} })^x=2^{ frac{3}{2} }\ 2^{ frac{1}{2}x }=2^{ frac{3}{2} }\ frac{1}{2}x= frac{3}{2} \ x=3[/latex] 2 [latex]a^{ frac{1}{2} }=2 /^2\ a=4\ \ a^6=8 / ^{ frac{1}{6} }\ a=(8^ frac{1}{3} )^ frac{1}{2} =2 ^frac{1}{2} = sqrt{2} \ \ a^{-5}=32 /^{- frac{1}{5} }\ a= sqrt[5]{ frac{1}{32} } = frac{1}{2} [/latex]