Solution set of the inequality log 3(x+2)(x+4)+ log 1 / 3(x+2)

Question

Solution set of the inequality log 3(x+2)(x+4)+ log 1 / 3(x+2) < (1/2) log √3 7(1) is (A) (-2,-1) (B) (-2,3) (C) (-1,3) (D) (3, ∞)

Tardigrade Admin · Accepted Answer

(x+2)(x+4) > 0 . x+2 > 0 ⇒ x > -2 Now (1) can be written as log 3(x+2)(x+4)- log 3(x+2) < (( log 7) / 2/( log 3) / 2) ⇒ log 3(x+4) < log 3 7 ⇒ x+4 < 7 or x < 3

Q. Solution set of the inequality $lo g_{3} (x + 2) (x + 4) + lo g_{1/3} (x + 2) < \frac{1}{2} lo g 37 (1)$ is

(-2,-1)

(-2,3)

(-1,3)

$(3, \infty)$

$(x + 2) (x + 4) > 0. x + 2 > 0$
$\Rightarrow x > - 2$
Now (1) can be written as
$lo g_{3} (x + 2) (x + 4) - lo g_{3} (x + 2) < \frac{( l o g 7 ) /2}{( l o g 3 ) /2}$
$\Rightarrow lo g_{3} (x + 4) < lo g_{3} 7$
$\Rightarrow x + 4 < 7$ or $x < 3$

Q. Solution set of the inequality log3​(x+2)(x+4)+log1/3​(x+2)<21​log3​7(1) is