помогите решить ур-ие

Ответ
4*log(x) 3 - 3*log(3x) 3 = 1
ОДЗ: x - любое
4 * 1/log(3) x - 3 * 1/log(3) 3x = 1
4 / log(3) x - 3 / [log(3) 3 + log(3) x] = 1
4 / log(3) x - 3 / [1 + log(3) x] = 1
log(3) x = a
4/a - 3/(1+a) = 1
4*(1+a) - 3a = a*(1+a)
4 + 4a - 3a = a + a^2
a^2 -4a + 3a + a - 4 = 0
a^2 = 4
a = +- 2
log(3) x = a
log(3) x = +2 => x = 3^2 = 9
log(3) x = -2 => x = 3^(-2) = 1/3^2 = 1/9
x1 = 9, x2 = 1/9