1 Oblicz a. log 100 + log 4 [latex] frac{1}{16} [/latex] b. log [latex] 10^{7} [/latex] - log 0,5 8 c. log 6 [latex] frac{1}{36} [/latex] + log [latex] sqrt[3]{10} [/latex] d. log [latex] sqrt[4]{10} [/latex] - log 3 [latex] sqrt[4]{3} [/latex] e. lo

[latex]a) log100+log_{4}frac{1}{16} = log10^{2}+log_{4}4^{-2} = 2+(-2) = 2-2 = 0\\b) log10^{7}-log_{0,5}8 = 7 - log_{frac{1}{2}}(frac{1}{2})^{-3}} =7-(-3) = 7+3 = 10\\c) log_{6}frac{1}{36}+logsqrt[3]{10} =log_{6}6^{-2}+log10^{frac{1}{3}} =-2+frac{1}{3} = -1frac{2}{3}\\d) logsqrt[4]{10}-log_{3}sqrt[4]{3} = log10^{frac{1}{4}}-log_{3}3^{frac{1}{4}}=frac{1}{4}-frac{1}{4} = 0\\e) log_{1,5}frac{9}{4}-log1 = log_{frac{3}{2}}(frac{3}{2}})^{2}-log10^{0} = 2-0 = 2[/latex] [latex]f) log_{frac{2}{3}}1,5-logsqrt{10} = log_{frac{2}{3}}frac{3}{2}-log10^{frac{1}{2}}=log_{frac{2}{3}}(frac{2}{3})^{-1}-frac{1}{2}=-1-(-frac{1}{2})=-1+frac{1}{2}=-frac{1}{2}[/latex]