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Question: The value of 'a' for which the equation ln (a lnx) = lnx has solution is-...

The value of 'a' for which the equation

ln (a lnx) = lnx has solution is-

A

1e\frac{1}{e}

B

1e2\frac{1}{e^{2}}

C

e

D

None of these

Answer

e

Explanation

Solution

Q a lnx = x ̃ lnx =xa\frac{x}{a}

The line y = xa\frac{x}{a} becomes tangent to

curve y = lnx at x = e for a = e