Вычислите: 1. [latex] \frac{ log_{8}20 }{ log_{8}5 } + log_{5}0,05 [/latex] 2. [latex] log_{16}log _{6}36 [/latex] 3. [latex]( 8^{ \frac{1}{3}log _{2}3 } ): log_{2}log _{3}81 [/latex]

[latex] \frac{\log_{8}20 }{\log_{8}5 } + \log_{5}0,05 = \log_{5}20+log_{5}20^{-1} = \log_{5}20-\log_{5}20 = 0;[/latex] [latex]\log_{16}\log _{6}36 = \log_{2^4}\log _{6}6^2 = \frac{1}{4}log_{2}(2\log _{6}6) = \frac{1}{4}log_{2}2 = \frac{1}{4};[/latex] [latex]( 8^{\frac{1}{3}+\log _{2}3 } ): \log_{2}\log _{3}81=((2^3)^{\frac{1}{3}}\cdot(2^3)^{\log _{2}3 } ): \log_{2}4=2\cdot3^3:2=27.[/latex]