Question

log6(4x^2-18x)=2
log3(-x+5)<3

Answer 1

log6 (4x^2 - 18x) = 2
log6 (4x^2 - 18x) = log6 (36)
ОДЗ
4x^2 - 18x > 0 
x ∈ ( - ∞; 0) ∪ (4,5; + ∞)

4x^2 - 18x = 36
4x^2 - 18x - 36 = 0   /:2
2x^2 - 9x - 18 = 0 
D = 225 = 15^2
x1 = ( 9 + 15)/4 = 6
x2 = ( 9 - 15)/4 = - 1,5

Ответ
- 1,5;   6

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log3 ( - x + 5) < 3 
log3 (-  x+ 5 ) < log3 (27)
ОДЗ
x < 5 

- x + 5 < 27
- x < 22
x > - 22

+ ОДЗ
x ∈ (  - 22;  5)

Ответ
x ∈ (  - 22;  5)