If log 12( log 7 x)

Question

If log 12( log 7 x)<0, then x belongs to (A) (1, ∞) (B) (1,7) (C) (1, ∞). (D) (1,7).

Tardigrade Admin · Accepted Answer

Given, log 12( log 7 x)<0 is defined when log 7 x>0 x>70 ⇒ x>1 log 12( log 7 x)<0 ⇒ log 7 x<12° ⇒ log 7 x<1=x<71 ⇒ x<7 From Eqs. (1) and (2), we get x ∈(1,7).

Q. If $lo g_{12} (lo g_{7} x) < 0$ , then $x$ belongs to

$(1, \infty)$

$(1, 7)$

$(1, \infty) .$

$(1, 7) .$

Given, $lo g_{12} (lo g_{7} x) < 0$ is defined when $lo g_{7} x > 0$
$x > 7^{0} \Rightarrow x > 1$
$lo g_{12} (lo g_{7} x) < 0 \Rightarrow lo g_{7} x < 1 2^{\circ}$
$\Rightarrow lo g_{7} x < 1 = x < 7^{1} \Rightarrow x < 7$
From Eqs. (1) and (2), we get $x \in (1, 7)$ .

Q. If log12​(log7​x)<0, then x belongs to

(1,∞)

(1,7)

(1,∞).

(1,7).