JEE Mains · Maths · STD 11 - 8. sequence and series
If \(\log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7}{2}\right)\) are in an arithmetic progression, then the value of \(x\) is equal to \(.....\)
- A \(1\)
- B \(4\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(2 \log _{3}\left(2^{x}-5\right)=\log _{3} 2+\log _{3}\left(2^{x}-\frac{7}{2}\right)\) Let \(2^{\mathrm{x}}=\mathrm{t}\) \(\log _{3}(t-5)^{2}=\log _{3} 2\left(t-\frac{7}{2}\right)\) \((t-5)^{2}=2 t-7\) \(t^{2}-12 t+32=0\) \((t-4)(t-8)=0\)…
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