Oblicz: a)[latex] log_{ sqrt{3} } 27=[/latex] b)[latex] log_{ sqr{ frac{1}{2} } } 32=[/latex] c)[latex] log_{7} 98- log_{7} 2 =[/latex] d)[latex]log_{6} 4 + log_{6} 9=[/latex] e)[latex]2 log5+2log2=[/latex][latex] log_{0,01} 10000=[/latex]

[latex]log_{sqrt{3}}27=log_{sqrt{3}}3^3=log_{sqrt{3}}(sqrt{3})^6=6[/latex] [latex]log_{frac{1}{2}}32=log_{frac{1}{2}}2^5=log_{frac{1}{2}}(frac{1}{2})^{-5}=-5[/latex] [latex]log_798-log_7 2=log_7(frac{98}{2})=log_7 49=log_7 7^2=2[/latex] [latex]log_6 4+log_6 9=log_6(4 cdot 9)=log_6 36=log_6 6^2=2[/latex] [latex]2log5+2log2=log5^2+log2^2=log 25+log4=log(25 cdot 4)=\ =log 100=log 10^2=2[/latex] [latex]log_{0,01}10000=log_{frac{1}{100}}10000=log_{frac{1}{100}}(frac{1}{100})^{-2}=-2[/latex]