If logx a, a^(x/2) and logbx are in GP, then x is equal to : -Maths 9th

If logx a, a^(x/2) and logbx are in GP, then x is equal to : -Maths 9th
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(b) loga (loge a) – loga (loge b)  logxa, \(a^{rac{x}{2}}\), logbx are in GP ⇒ \(\big[a^{rac{x}{2}}\big]^2\) = logxa . logbx⇒ ax = \(rac{ ext{log}\,a}{ ext{log}\,x}.rac{ ext{log}\,x}{ ext{log}\,b}\)⇒ ax = \(rac{ ext{log}\,a}{ ext{log}\,b} = ext{log}_b\,a\) ⇒ x = loga (logba)= log a = \(rac{ ext{log}_e\,a}{ ext{log}_e\,b}\) = loga (loge a) – loga (loge b)
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