Oblicz a [latex]log_{ frac{1}{8} } 64[/latex] b) [latex] logfrac{1}{2} 2 sqrt{2} [/latex] c)[latex] log_{ sqrt{2} } 0,125[/latex]

[latex]a)\\log_{frac{1}{8}}64=x\\(frac{1}{8})^{x}=64\\(frac{1}{8})^{x}=8^{2}\\(frac{1}{8})^{x}=(frac{1}{8})^{-2}\\x=-2[/latex] [latex]b)\\log_{frac{1}{2}}2sqrt{2}=x\\(frac{1}{2})^{x}=2sqrt{2}\\(frac{1}{2})^{x}=2^{1}cdot2^{frac{1}{2}}\\(frac{1}{2})^{x}=2^{frac{3}{2}}\\(frac{1}{2})^{x}=(frac{1}{2})^{-frac{3}{2}}\\x=-frac{3}{2}[/latex] [latex]c)\\log_{sqrt{2}}0,125=x\\(sqrt{2})^{x}=0,125\\(sqrt{2})^{x}=frac{1}{8}\\(2^{frac{1}{2}})^{x}=(frac{1}{2})^{3}\\2^{frac{1}{2}x}=2^{-3}\\frac{1}{2}x=-3\\x=-6[/latex]