WBJEE · Maths · Sequences and Series
If \(x\) is a positive real number different from 1 such that \(\log _{a} x, \log _{b} x, \log _{c} x\) are in \(\mathrm{AP}\), then
- A \(b=\frac{a+c}{2}\)
- B \(b=\sqrt{a c}\)
- C \(c^{2}=(a c)^{log_{a} b}\)
- D None of these
Answer & Solution
Correct Answer
(C) \(c^{2}=(a c)^{log_{a} b}\)
Step-by-step Solution
Detailed explanation
Given, \(\log _{a} x, \log _{b} x\) and \(log_{c}\) \(x\) are in \(A P\). \(\therefore \quad 2 \log _{b} x=\log _{a} x+\log _{c} x\)…
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