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Question

Solve the equation
(a42a2b2+b4)x1=(ab)2x(a+b)2.

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Solution

(a42a2b2+b4)x1=(ab)2x(a+b)2
Applying log on both the sides gives
(x1)log(a42a2b2+b4)=2xlog(ab)2log(a+b)(x1)log(a2b2)2=2xlog(ab)2log(a+b)2(x1)log(a2b2)=2xlog(ab)2log(a+b)2(x1)(log(a+b)+log(ab))=2xlog(ab)2log(a+b)xlog(a+b)=log(ab)x=log(ab)log(a+b)

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