Question

Решите пжлст!
log3(x)*log2(x)=4log3(2)
И вот это
log5(x)*log3(x)=9log5(3)

Answer 1

1) Используем равенство log2(x) = log3(x)/log3(2):
log3(x) * log3(x)/log3(2) = 4log3(2)
(log3(x))^2 = (2log3(2))^2
(log3(x))^2 = (log3(4))^2
log3(x) = log3(4) или log3(x) = -log3(4)
x = 4 или x = 1/4

2) log5(x) = log3(x)/log3(5) = log3(x) * log5(3)
log3(x) * log3(x) * log5(3) = 9log5(3)
(log3(x))^2 = 9
log3(x) = 3 или log3(x) = -3
x = 3^3 или x = 3^(-3)
x = 27 или x = 1/27