Question

2 log7 (x-2)=-2+log7 (x-10) 

Answer 1

Решение
2 log₇ (x-2) = - 2 + log₇ (x - 10)
2 log₇ (x-2) = - 2log₇ 7 + log₇ (x - 10)
log₇ (x-2)² = log₇ 7⁻² + log₇ (x - 10)
log₇ (x-2)² = log₇ [(1/49) * (x - 10)]
(x - 2)² = (1/49) * (x - 10)
49*(x² - 4x + 4) = x - 10
49x² - 196x + 196 - x + 10 = 0
49x² - 197x + 206 = 0
D = 30889 - 4*49*206 = 30889 - 40376 = - 9487 < 0 решений нет