COMEDK · Maths · 1. Basic of Mathematics
The value of \(a^{\log _b c}-c^{\log _b a}\), where \(a, b, c>0\) but \(a, b, c \neq 1\), is
- A b
- B a
- C c
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
Let \(x = a^{\log_{b} c}\). Taking the logarithm with base \(b\) on both sides, we get: \(\log_{b} x = \log_{b} (a^{\log_{b} c})\) Using the property \(\log_{b} (m^n) = n \log_{b} m\), we have: \(\log_{b} x = (\log_{b} c) \times (\log_{b} a)\) Similarly, let…
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