Question

Let a, b, c be three numbers in G. P . And we take theirs log (eg. Log a, Log b,Log c) is it always true that their log will be in A. P?

Answer 1

Please refer to a Proof in the Explanation.

Explanation:

`a,b,c` are in GP.

`:."The common ratio"=b/a=c/b`.

Clearly, `b^2=ac`.

`Logb^2=Log(ac)`.

`:. 2Logb=Loga+Logc`.

Consequently, `loga, logb and logc` are in AP.