oblicz: a) [latex]log_{5} sqrt{5} [/latex] b) [latex]log_{3}3 sqrt{3} [/latex] c) [latex]log_{2}4 sqrt[3]{16} [/latex] d) [latex]log_{3} frac{1}{3} sqrt[3]{3} [/latex] e) [latex]log_{2} 0,125 sqrt[6]{64} [/latex] f) [latex]log sqrt{0,001} [/latex]

[latex]log_5sqrt5=frac{1}{2}\log_33sqrt3=log_3(3*3^{frac{1}{2}})=log_3(3^{frac{3}{2}})=frac{3}{2}\log_2(4*sqrt[3]{2^4})=log_2(2^2*2^{frac{4}{3}})=log_2(2^{frac{10}{3}})=frac{10}{3}\log_3(3^{-1}*3^{frac{1}{3}})=log_3(3^{-frac{2}{3}})=-frac{2}{3}\log_2(frac{1}{8}*sqrt[6]{2^6})=log_2(2^{-3}*2)=log_22^{-2}=-2\logsqrt{0,001}=logsqrt{0,1^3}=\=log(0,1)^{frac{3}{2}}=log10^{-frac{3}{2}}=-frac{3}{2}[/latex]