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Question

If (lnx+1)(2lnx3)(lnx2)=α2lnx3+βlnx2then α2β2=...

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Solution

(lnx+1)(2lnx3)(lnx2)=α2lnx3+βlnx2(lnx+1)=α(lnx2)+β(2lnx3)
For x=e2 we get β=3
And for x=e3/2 we get α=5
Therefore, α2β2=259=16

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