Question

Помогите решить!
log(5)x>log(x)25

Answer 1

log(a) b = 1/log(b) a

log(a) b^n = n*log(a) b

log(5)x>log(x)25

ОДЗ x>0 x≠1

log(5)x > 2log(x) 5

log(5)x - 2/log(5)x > 0

log(5)x = t

t - 2/t > 0

(t^2-2)/t > 0

(t - √2)(t + √2)/t > 0

---------------- (-√2) +++++++++ (0) ---------------- (√2) +++++++

t∈(-√ 2  0) U (√2  + ∞)

1/ log(5) x > -√2

x > 5^(-√2)

2/ log(5)x < 0

x < 1

3/ log(5) x > √2

x> 5^(√2)

ответ x∈(1/5^(√2)  1) U (5^(√2) +∞)