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if logx a, logx b, logx c, are in AP, prove it a, b, c are in GP
If log a,log b and log c are in A.P then,Using property of AP,2log b=log a+log cor, log b^2 = log (ac)or, b^2 = acThe resultant expression is the general expression of G.P.Therefore a,b,c are in G.P
Loga logb logc are in AP i.e. 2logb=loga + logcNow that gives logb^2=log(a*c)Thus takin both sides on x power gives b^2 =acThat proves a,b,c are in GP
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