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Question

If logx a, ax2 and logbx are in G.P. then write the value of x.


Solution

logx a,ax2,x are in G.P.

[an2]2=logxa.logbx

=log alog x.log xlog b

ax=log alog b   [Using logyx=log xlog y]

taking log on both sides.

logax=log(log alog b)

x log a=log(log alog b)

x=log(logba)log a

x=loga(logba)

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