Oblicz a) [latex]log _{5} 5 sqrt[3]{5} [/latex] - tylko ta mała 5 przy log ma być pod pierwiastkiem b) [latex]log _{2} 8sqrt{2} = [/latex] c) [latex]log _{ frac{1}{3} } 81 sqrt{3} = [/latex] d) [latex]log_{4} 8 sqrt[4]{2} = [/latex]

[latex]log_{ sqrt{5}}5 sqrt[3]{5}= log_{ sqrt{5}} 5*5^{ frac{1}{3}}=log_{ sqrt{5}} 5^{ frac{4}{3}}=log_{{5^ frac{1}{2}}} 5^{ frac{4}{3}}\\ (5^ frac{1}{2} )^x=5^ frac{4}{3}\ 5^{ frac{1}{2}x}=5^ frac{4}{3}\ frac{1}{2} x= frac{4}{3}\ x= frac{8}{3} \ x= 2 frac{2}{3} [/latex] [latex]log_28 sqrt{2}=log_28*2^ frac{1}{2}=log_22^3*2^ frac{1}{2}=log_22^ frac{7}{2}\ 2^x=2^ frac{7}{2} \ x= frac{7}{2} \ x= 3,5 [/latex] [latex]log_{ frac{1}{3}}81 sqrt{3}=log_{ frac{1}{3}}3^4*3^ frac{1}{2}=log_{ frac{1}{3}}3^ frac{9}{2}=log_{ frac{1}{3}} (frac{1}{3}) ^{- frac{9}{2}} \ ( frac{1}{3})^x= (frac{1}{3})^ {-frac{9}{2}} \ x=- frac{9}{2}\ x=-4,5 [/latex] [latex]log_48 sqrt[4]{2}=log_42^3*2^ frac{1}{4}=log_{2^2}2^ frac{13}{4}\ (2^2)^x=2^ frac{13}{4}\ 2^{2x}=2^ frac{13}{4}\ 2x= frac{13}{4}\ x= frac{13}{8}\ x=1 frac{5}{8} \ Licze na naj :)[/latex]