WBJEE · Maths · Basic of Mathematics
If \(\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)\), then
- A \(4 < x \leq 5\)
- B \(x < -4\) or \(x>4\)
- C \(-1 \leq x \leq 5\)
- D \(x < -1\) or \(x>5\)
Answer & Solution
Correct Answer
(C) \(-1 \leq x \leq 5\)
Step-by-step Solution
Detailed explanation
Given, \(\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)\) if and only if \(\begin{array}{l} x^{2}-16 \leq 4 x-11 \\ \Rightarrow x^{2}-4 x-5 \leq 0 \\ x^{2}-5 x+x-5 \leq 0 \\ \Rightarrow x(x-5)+1(x-5) \leq 0 \\ (x-5)(x+1) \leq 0 \end{array}\) Sign scheme of…
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