3log^2√2x-14log√2x-5=0помогите решить

Question

3log^2√2x-14log√2x-5=0помогите решить

Answer 1

Решение
3log^2√2x-14log√2x-5=0
ОДЗ:  x > 0
log√2x = t
3t² - 14t - 5 = 0
D = 196 + 4*3*5 = 256
t₁ = (14 - 16)/6 = - 1/3
t₂ = (14 + 16)/6 = 5
1)  log√2x = - 1/3
x = (√2)⁻¹/³
x = 1/(2)¹/⁶
2)   log√2x = 5
x = (√2)⁵
x = √(2⁵) = 4√2