А)
log₀.₇(5x-9) = 0
0.7° = 5x - 9
5х - 9 = 1
5х = 1 + 9
5х = 10
х = 10 : 5
х = 2
Ответ: х = 2.
b)
log₂x + log₂(5x - 1) = 2
log₂(x · (5x - 1)) = 2
log₂(5x² - x) = 2
2² = 5x² - x
5х² - х - 4 = 0
D = (-1)² - 4 · 5 · (- 4) = 81 = 9²
х₁ = (1 + 9) / (2 · 5) = 10/10 = 1
х² = (1 - 9) / (2 · 5) = - 8/10 = - 0,8; - не подходит.
Ответ: х = 1.
c)
log₁₃(5 - x) = log₁₃(4x + 25)
5 - х = 4х + 25
4х + х = 5 - 25
5х = - 20
х = - 20 : 5
х = - 4
Ответ: х = - 4.