Question

log²снизу5(x-1)-log снизу 5(x-1)³=-2

Answer 1

log₅²(x - 1) - log₅²(x - 1)³ = - 2
log₅²(x - 1) - 3log₅²(x - 1) + 2 = 0
t = log₅(x - 1)
t² - 3t + 2 = 0
D = 9 - 8 = 1
t₁ = 0.5(3 - 1) = 1
t₂ = 0.5(3 + 1) = 2
log₅(x - 1) = 1  ---> x - 1 = 5 ---> x₁ = 6
log₅(x - 1) = 2  ---> x - 1 = 25 ---> x₂ = 26