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if three positive integers a, b, c are in G.P., then log a, log b, log c are in

if three positive integers a, b, c are in G.P., then log a, log b, log c are in Correct Answer A.P.

Concept:

  •  A Geometric progression is a sequence of numbers in which each term after the first term is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. 

  •  An arithmetic progression is a sequence of numbers in which the difference between any two successive members is a constant, which is called a common difference.

Formula used:

  • log x + log y = log xy

  • log xa = a.log x

Explanation:

Since a, b, c are in G.P., then, 

b2 = ac

Applying logarithm to this equation, we get,

log (b2) = log (ac)

⇒ 2 log b = log a + log c, which satisfies the condition of an A.P. i.e., 2q = p + r, where p, q, r in the A.P. 

⇒ log a, log b, log c are in A.P.

Hence, if three positive integers a, b, c are in G.P., then log a, log b, log c are in A.P.

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