Question

1)lg(13x-x^2)>2 lg 2+2 lg 3
2)log9(x^2-6x+8)⩽0,5

Answer 1

1)
lg (13x - x²) > 2 lg 2 + 2 lg 3
lg (13x - x²) > lg 4 + lg 9
lg (13x - x²) > lg 36
13x - x² > 36
x² - 13x + 36 < 0
(x - 4)(x - 9) < 0
x ∈ (4; 9)

2)
log₉(x² - 6x + 8) ≤ 0,5
0 < x² - 6x + 8 ≤ 3
$left { {{x^2-6x+8 textgreater 0} atop {x^2-6x+5 leq 0}} right. \ \ left { {{(x-2)(x-4) textgreater 0} atop {(x-1)(x-5)leq 0}} right. \ \left { {{xE(-oo; 2)U(4;+oo)} atop {xE[1;5]}} right.$
x ∈ [1 ; 2) ∪ (4 ; 5]