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Question 11

Mathematics Sequence And Series Hard

If a, b, c are in geometric progression, then log<sub>ax</sub> x, log<sub>bx</sub> x and log<sub>cx</sub> x are in

(A) Arithmetic progression
(B) Geometric progression
(C) Harmonic progression
(D) Arithmetico-geometric progression
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

\(\log_{ax}x = \frac{1}{\log_x(ax)} = \frac{1}{\log_x a + 1}\). The same holds for b and c.

a, b, c are in GP, so \(\log_x a, \log_x b, \log_x c\) are in AP. Adding 1 to each keeps them in AP.

The given terms are the reciprocals of an AP, so they are in harmonic progression.

Answer: (C) Harmonic progression

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