Answer :


a, b and c are in GP

b2 = ac {property of geometric mean}

Taking log on both sides with base m –

logm b2 = logm ac

logm b2 = logm a + logm c {using property of log}

2logm b = logm a + logm c …equation 1

Note: If three numbers a,b and c are in AP,we can say that –

2b = a + c

As equation 1 matches the form above, So

logm a, logm b and logm c are in AP. …(1)

Now, applying base changing formula we get

logab =

Applying base change on 1, we get

are in A.P

Hence, proved

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