Question

If $\log _{12}\left(\log _7 x\right)<0$, then $x$ belongs to

• A. $(1, \infty)$
• B. $(1,7)$
• C. $(1, \infty).$
• D. $(1,7).$

Answer 1

Answer: (B)

Given, $\log _{12}(\log _7 x)<0$ is defined when $\log _7 x>0$
$x>7^0 \Rightarrow x>1 $
$\log _{12}(\log _7 x)<0 \Rightarrow \log _7 x<12^{\circ} $
$\Rightarrow \log _7 x<1=x<7^1 \Rightarrow x<7$
From Eqs. (1) and (2), we get $x \in(1,7)$.