Q103 / 155 · WBJEE 2022 · Mathematics
If $x$ satisfies the inequality $\log _{25} x^2+\left(\log _5 x\right)^2 < 2$, then $x$ belongs to
- A$\left(\frac{1}{5}, 5\right)$
- Correct answerB$\left(\frac{1}{25}, 5\right)$
- C$\left(\frac{1}{5}, 25\right)$
- D$\left(\frac{1}{25}, 25\right)$
Solution
Domain $=(0, \infty)$
$\begin{aligned}
&\log _5 x+\left(\log _5 x\right)^2-2 < 0 \\
&\Rightarrow\left(\log _5 x-1\right)\left(\log _5 x+2\right) < 0 \\
&\therefore-2 < \log _5 x < 1 \\
&\therefore \frac{1}{25} < x < 5
\end{aligned}$
Hence, the correct answer is option: 'B'.