WBJEE · Maths · Basic of Mathematics
If \(x\) satisfies the inequality \(\log _{25} x^2+\left(\log _5 x\right)^2 < 2\), then \(x\) belongs to
- A \(\left(\frac{1}{5}, 5\right)\)
- B \(\left(\frac{1}{25}, 5\right)\)
- C \(\left(\frac{1}{5}, 25\right)\)
- D \(\left(\frac{1}{25}, 25\right)\)
Answer & Solution
Correct Answer
(B) \(\left(\frac{1}{25}, 5\right)\)
Step-by-step Solution
Detailed explanation
Domain \(=(0, \infty)\) \(\begin{aligned} &\log _5 x+\left(\log _5 x\right)^2-2 < 0 \\ &\Rightarrow\left(\log _5 x-1\right)\left(\log _5 x+2\right) < 0 \\ &\therefore-2 < \log _5 x < 1 \\ &\therefore \frac{1}{25} < x < 5 \end{aligned}\)
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