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Question

If a2=b3=c5=d6 then show that logabcd=315

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Solution

Atfirsta2=d6a=(d6)12b3=d6a=(d6)13c5=d6a=(d6)15Now,substitutethevalueofa,b,andcintermdinthelogarithmicterm.logdabc=logd(d6)12(d6)13(d6)15=logd(d6)12+13+15(byusingproductruleofonents)=logd(d6)15+10+630=logd(d6)3130=logd(d)6×3130=logd(d)315Byusingpowerruleoflogarithms=315×logdd=315×1[Byusinglogarithmofbaserule]=315Hence,logdabc=315proved.

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