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?

1 Answer
Aug 4, 2018

Please refer to a Proof in the Explanation.

Explanation:

a,b,ca,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.