Identify Logarithm Properties: Identify the properties of logarithms that can be applied to the problem. The natural logarithm of the reciprocal of e can be simplified using the property ln(1/x) = -ln(x).Apply Logarithm Property: Apply the logarithm property to the given problem. ln((1)/(e)) = -ln(e)Simplify Natural Logarithm: Simplify the natural logarithm of e. Since ln(e) is equal to 1, we have -ln(e) = -1.Conclude Solution: Conclude the solution. The value of ln((1)/(e)) is -1.

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$\ln \left( \frac{1}{e} \right)$

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Precalculus

Evaluate rational exponents

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\ln \left( \frac{1}{e} \right)

Identify Logarithm Properties: Identify the properties of logarithms that can be applied to the problem. $\newline$ The natural logarithm of the reciprocal of $e$ can be simplified using the property $\ln(\frac{1}{x}) = -\ln(x)$ .
Apply Logarithm Property: Apply the logarithm property to the given problem. $\newline$ $\ln\left(\frac{1}{e}\right) = -\ln(e)$
Simplify Natural Logarithm: Simplify the natural logarithm of $e$ . $\newline$ Since $\ln(e)$ is equal to $1$ , we have $-\ln(e) = -1$ .
Conclude Solution: Conclude the solution. $\newline$ The value of $\ln\left(\frac{1}{e}\right)$ is $-1$ .