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Fundamental Laws of Logarithms

The positive ...

Question

The positive value of $k$ for which $k e^{x} - x = 0$ has only one roots is

\frac{1}{e}

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1

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e

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{log}_{e} 2

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Solution

The correct option is A $\frac{1}{e}$
$\begin{matrix} k e^{x} - x = 0 d i f f . w . r . t x K . e^{x} - 1 = 0 k . e^{x} = 1 e^{x} = \frac{1}{k} k = \frac{1}{e} \end{matrix}$

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