Вычислить [latex]log_{3} 4*log_{4}5*log _{5} 7*log_{7} 81[/latex]

[latex]log_{3}4 * log_{4}5 * log_{3}7 * log_{7}81 = [/latex] [latex]= \frac{log_{4}5}{log_{4}3} * \frac{log_{7}81}{log_{7}5} =[/latex] [latex]= log_{3}5 * log_{5}81 = 4 * log_{3}5 * log_{5}3 = 4 * \frac{log_{3}5}{log_{3}5} = 4[/latex] [latex]log_{5}81 = log_{5}(3^4) = 4log_{5}3[/latex]