Решите уравнение (log (3) √x+8) - 1 = log (3) 2-log (3) √x-8

(log₃√ (x+8)) - 1 = log₃2-log₃√ (x-8) ОДЗ х+8>0 x > - 8 x-8>0 x >8

1/2log₃ (x+8) - 1 = log₃2 - 1/2log₃ (x-8)

1/2log₃ (x+8) + 1/2log₃ (x-8) = log₃2 + 1

1/2 * (log₃ (x+8) + log₃ (x-8) = log₃2 + log₃3

log₃ (x+8) * (x-8) = 2 * log₃2*3

log₃ (x²-8²) = log₃6²

х²-64=36

х²=100

х₁=10 х₂ = - 10

Ответ с учетом ОДЗ х=10