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Prove that : logea-logeb=2[(a-b)/(a+b)+1...

Prove that : `log_ea-log_eb=2[(a-b)/(a+b)+1/3((a-b)/(a+b))^3`+1/5((a-b)/(a+b))^5+...],a > b`

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Let`(a-b)/(a+b)=a` in the R.H.S.`thereforeR.H.S.=2[x+x^2/3+x^5/5+...]=log((1+x)/(1-x))=log(1+(1-b)/(a+b)/1-(a-b)/(a+b))=log((2a)/(ab))=loga-logb=L.H.S`
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