Log1/6(10 – x) + log1/6(x – 3) ≥ - 1.

Question

Log1/6(10 – x) + log1/6(x – 3) ≥ - 1.

Answer 1

Log₁/₆(10-x)+log₁/₆(x-3)≥-1
ОДЗ:  10-x>0  x<10   x-3>0  x>3   x∈(3;10)
log₁/₆(10-x)(x-3)≥log₁/₆6
-x²+13x-30≤6  I×(-1)
x²-13x+36≥0  D=25
x₁=4    x₂=9
(x-4)(x-9)≥0
-∞_____+_____4_____-_____9_____+______+∞
x∈(-∞;4]U[9;+∞)
Учитывая ОДЗ х∈(3;4]U[9;10).