Answer :

Given:


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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