Нужно решить уравнения (и обязательно - ОДЗ)

1. Log x по основанию 2 * log x по основанию 3 = 4Log 3 по основанию 2

2. Log x по основанию 3 * log x по основанию 4 = 4log 3 по основанию 4

log2 (x) * log3 (x) = 4log2 (3) log2 (x^log3 (x)) = log2 (3^4) = > x^ (log3 (x)) = 3^4

представим 3^4=t = >t=x^logx (t) = >x^ (log3 (x)) = x^logx (t) = >log3 (x) = logx (t)

log3 (x) = 1/logt (x) = >log3 (x) * logt (x) = 1 = > log3 (x) * log3^4 (x) = 1 1/4 (log3 (x)) ^2=1

(log3 (x)) ^2=4 log3 (x) = + - 2 x1=9 x2=1/9 одз х>0

2) log3 (x) * log4 (x) = 4log4 (3) log4 (x^log3 (x)) = log4 (3^4) x^log3 (x) = 3^4 x^log3 (x) = x^ (logx (3^4) log3 (x) = logx (3^4) log3 (x) = 4logx (3) log3 (x) = 4/log3 (x)

(log3 (x) ^2=4 log3 (x) = + - 2 log3 (x) = - 2 x1=3^-2=1/9 x2=3^2=9