If logax,logbx logcx are in A.P. where  x not equal to 1, show that c2= (ac)log a

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Please find below the solution to the asked query:

We havelogax,logbx, logcx in A.P.Hence2logbx=logax+ logcx2logxb=1logxa+1logxc2logxb=logxa+logxclogxa.logxc2logxc=logxblogxalogxaclogxc2=logablogxaclogxc2=logxaclogabc2=aclogab

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