Question

50 баллов матеша помогите пж

Answer 1

log2/9 x = log9 x^2 + 8

log2/9 x = log9 (x^2 / 81) + 8

log2/9 x = log9 (x/9)^2 + 8

log2/9 x = 2 log9 (x/9) + 8

log2/9 x - 2 log9 (x/9) = 8

log2/9 x - log9 (x/9)^2 = 8

log2/9 (x / (x/9)^2) = 8

log2/9 (x / (x^2 / 81)) = 8

log2/9 (81 / x) = 8

log2/9 81 - log2/9 x = 8

4 - log2/9 x = 8

log2/9 x = -4

x = 2^-4 * 9^2

x = 1/81 * 81

x = 1

Ответ: х = 1