Simplify ln((1)/(e^(4))) Answer:

Identify Components: Identify the components of the expression ln((1)/(e^(4))). In ln((1)/(e^(4))), we have a natural logarithm of a fraction where the denominator is e raised to the power of 4.Apply Power Rule: Apply the logarithm power rule. The power rule of logarithms states that ln(a^b) = b*ln(a). We can apply this rule in reverse since the denominator is e raised to the power of 4. ln((1)/(e^(4))) = ln(1) - ln(e^(4))Simplify Logarithms: Simplify the logarithms. We know that ln(1) = 0 because e^0 = 1. Also, ln(e^(4)) = 4 because the base of the natural logarithm is e. ln((1)/(e^(4))) = 0 - 4Perform Subtraction: Perform the subtraction. 0 - 4 = -4

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Simplify $\ln \left(\frac{1}{e^{4}}\right)$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Simplify

\ln \left(\frac{1}{e^{4}}\right)

\newline

Answer:

Identify Components: Identify the components of the expression $\ln\left(\frac{1}{e^{4}}\right)$ . In $\ln\left(\frac{1}{e^{4}}\right)$ , we have a natural logarithm of a fraction where the denominator is $e$ raised to the power of $4$ .
Apply Power Rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We can apply this rule in reverse since the denominator is $e$ raised to the power of $4$ . $\newline$ $\ln\left(\frac{1}{e^{4}}\right) = \ln(1) - \ln(e^{4})$
Simplify Logarithms: Simplify the logarithms. $\newline$ We know that $\ln(1) = 0$ because $e^0 = 1$ . Also, $\ln(e^{4}) = 4$ because the base of the natural logarithm is $e$ . $\newline$ $\ln\left(\frac{1}{e^{4}}\right) = 0 - 4$
Perform Subtraction: Perform the subtraction. $\newline$ $0 - 4 = -4$