Question

If three numbers be in G.P., then their logarithms will be in [BIT 1992]
A) A.P. B) G.P. C) H.P. D) None of these

Answer 1

Hello Dear!!!

Here's your answer...

Your required answer is option A.

=> AP

Here's the explanation...

x,y,z are in GP

then,

x/y = y/z

(y)^2 = xz

logarithm on both sides

log(y)^2=log(xz)

2log y = log x + log z = log y + log y

log y - log x = log z - log y

Therefore,

log x , log y , log z are in AP..

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Hope this helps you....

Answer 2

Let's take a,b,c

If they are in G.P, then b²=ac

Apply log on either sides,

2 log b = log a + log c

This is the condition for an A.P

So,  basically their logarithms are in AP