Simplify ln((1)/(e^(3))) Answer:

Identify Components: Identify the components of the natural logarithm expression. ln((1)/(e^(3))) Here, we have the natural logarithm of a fraction where the denominator is e raised to the power of 3.Apply Power Rule: Apply the logarithm power rule. The power rule of logarithms states that ln(a^b) = b*ln(a). In this case, we can apply the rule in reverse to move the exponent on e out in front of the logarithm. ln((1)/(e^(3))) = ln(1) - ln(e^(3))Simplify Logarithms: Simplify the logarithm of 1 and the logarithm of e to the power of 3. ln(1) is 0 because e^0 = 1. ln(e^(3)) is 3 because ln(e) = 1, and using the power rule, 3*ln(e) = 3*1 = 3. So, ln((1)/(e^(3))) = 0 - 3Calculate Final Result: Calculate the final result. 0 - 3 = -3

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Simplify $\ln \left(\frac{1}{e^{3}}\right)$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

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Q. Simplify

\ln \left(\frac{1}{e^{3}}\right)

\newline

Answer:

Identify Components: Identify the components of the natural logarithm expression. $\ln\left(\frac{1}{e^{3}}\right)$ Here, we have the natural logarithm of a fraction where the denominator is $e$ raised to the power of $3$ .
Apply Power Rule: Apply the logarithm power rule. $\newline$ The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . In this case, we can apply the rule in reverse to move the exponent on $e$ out in front of the logarithm. $\newline$ $\ln\left(\frac{1}{e^{3}}\right) = \ln(1) - \ln(e^{3})$
Simplify Logarithms: Simplify the logarithm of $1$ and the logarithm of $e$ to the power of $3$ .
$\ln(1)$ is $0$ because $e^0 = 1$ .
$\ln(e^{3})$ is $3$ because $\ln(e) = 1$ , and using the power rule, $3\cdot\ln(e) = 3\cdot1 = 3$ .
So, $e$ $0$
Calculate Final Result: Calculate the final result. $\newline$ $0 - 3 = -3$