Вычислите: 1. [latex] log_{0,2}125: log_{16}64* log_{3}81 [/latex] 2. [latex] log_{ frac{1}{2} }16* log_{5} frac{1}{25} : 9^{ log_{3} 2} [/latex] 3. [latex] log_{ frac{1}{3} }9* log_{2} frac{1}{8} : 7^{ 2log_{49} 2} [/latex] 4. [latex](3 log_{7} 2-log _{7} 24):( log_{7}3+ log_{7}9) [/latex]

[latex] log_{0,2}125: log_{16}64cdotlog_{3}81 = log_{5^{-1}}5^3: log_{2^4}2^6cdotlog_{3}3^4 =\= -3log_{5}5: frac{6}{4} log_{2}2cdot4log_{3}3 = -3cdotfrac{2}{3}cdot4=-8;[/latex][latex] log_{frac{1}{2} }16cdotlog_{5}frac{1}{25}:9^{log_{3}2} = log_{2^{-1}}2^4cdotlog_{5}5^{-2}:(3^2)^{ log_{3}2} =\= -4log_{2}2cdot(-2log_{5}5):(3^{ log_{3}2})^2 = -4cdot(-2):2^2=2; [/latex][latex]log_{frac{1}{3} }9cdotlog_{2}frac{1}{8}: 7^{2log_{49}2} = log_{3^{-1}}3^2cdotlog_{2}2^{-3}: 49^{log_{49}2} =\= -2log_{3}3cdot(-3log_{2}2): 2= -2cdot(-3): 2= 3;[/latex][latex](3log_{7} 2-log _{7} 24):(log_{7}3+ log_{7}9) = (log_{7} 2^3-log _{7} 24):log_{7}(3cdot9) =\= log_{7} frac{8}{24}:log_{7}27 = log_{7} 3^{-1}:log_{7}3^3 = -log_{7} 3:(3log_{7}3)=- frac{1}{3} .[/latex]