Simplify ln((1)/(e)) Answer:

Identify Properties: Identify the properties of logarithms that can be applied to the problem. The natural logarithm of 1 over e, ln((1)/(e)), can be rewritten using the property of logarithms that states ln(a/b) = ln(a) - ln(b).Apply Property: Apply the logarithm property to the given expression. ln((1)/(e)) = ln(1) - ln(e)Simplify Logarithms: Simplify the natural logarithm of 1 and the natural logarithm of e. ln(1) is always 0 because e^0 = 1, and ln(e) is always 1 because e^1 = e. So, ln(1) - ln(e) = 0 - 1Calculate Final Value: Calculate the final simplified value. 0 - 1 = -1

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Simplify $\ln \left(\frac{1}{e}\right)$ $\newline$ Answer:

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Precalculus

Evaluate rational exponents

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Q. Simplify

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

\newline

Answer:

Identify Properties: Identify the properties of logarithms that can be applied to the problem. $\newline$ The natural logarithm of $1$ over $e$ , $\ln\left(\frac{1}{e}\right)$ , can be rewritten using the property of logarithms that states $\ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)$ .
Apply Property: Apply the logarithm property to the given expression. $\newline$ $\ln\left(\frac{1}{e}\right) = \ln(1) - \ln(e)$
Simplify Logarithms: Simplify the natural logarithm of $1$ and the natural logarithm of $e$ . $\ln(1)$ is always $0$ because $e^0 = 1$ , and $\ln(e)$ is always $1$ because $e^1 = e$ . So, $\ln(1) - \ln(e) = 0 - 1$
Calculate Final Value: Calculate the final simplified value. $\newline$ $0 - 1 = -1$