[latex] log_{ frac{1}{2}}5* log_{5}16= log_{5}8-log{5} 1000 = log_{12}4+ log_{12}36= log9+2logfrac{1}{3}= log_{3}sqrt[4]{27} = [/latex]

[latex]log_frac{1}{2}5cdot log_516=frac{1}{log_5frac{1}{2}}cdot log_516=frac{log_52^4}{log_52^{-1}}=frac{4log_52}{-log_52}=-4\\log_58-log_51000=log_5frac{8}{1000}=log_5frac{1}{125}=log_55^{-3}=-3log_55=-3\\log_{12}4+log_{12}36=log_{12}(4cdot36)=log_{12}144=log_{12}12^2=2log_{12}12=2\\log9+2logfrac{1}{3}=log9+log(frac{1}{3})^2=log9+logfrac{1}{9}=log(9cdotfrac{1}{9})=log1=0\\log_3sqrt[4]{27}=log_3sqrt[4]{3^3}=log_33^frac{3}{4}=frac{3}{4}log_33=frac{3}{4}[/latex]

rozwiazania w zalaczeniu z tw o dzialaniu na log zad 1 ostatni zalacznik