Simplify e^(2ln 6) Answer:

Recognize Properties: Recognize the properties of logarithms and exponents. The expression e^(2ln 6) involves the natural logarithm ln, which is the logarithm to the base e. The property of logarithms that we can use here is that e^(ln x) = x for any x > 0. In this case, we have an additional factor of 2 in the exponent.Apply Power Rule: Apply the power rule for logarithms. The power rule for logarithms states that a*log_b(x) = log_b(x^a), where a is a real number, b is the base of the logarithm, and x is the argument of the logarithm. In this case, we can rewrite 2ln 6 as ln(6^2).Simplify Using Rule: Simplify the expression using the power rule. We have e^(ln(6^2)), which simplifies to e^(ln(36)) because 6^2 equals 36.Apply Property: Apply the property of logarithms and exponents. Using the property e^(ln x) = x, we can simplify e^(ln(36)) to just 36.

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Simplify $e^{2 \ln 6}$ $\newline$ Answer:

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Algebra 1

Evaluate integers raised to positive rational exponents

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Q. Simplify

e^{2 \ln 6}

\newline

Answer:

Recognize Properties: Recognize the properties of logarithms and exponents. $\newline$ The expression $e^{2\ln 6}$ involves the natural logarithm $\ln$ , which is the logarithm to the base $e$ . The property of logarithms that we can use here is that $e^{\ln x} = x$ for any x > 0. In this case, we have an additional factor of $2$ in the exponent.
Apply Power Rule: Apply the power rule for logarithms. $\newline$ The power rule for logarithms states that $a\log_b(x) = \log_b(x^a)$ , where $a$ is a real number, $b$ is the base of the logarithm, and $x$ is the argument of the logarithm. In this case, we can rewrite $2\ln 6$ as $\ln(6^2)$ .
Simplify Using Rule: Simplify the expression using the power rule. $\newline$ We have $e^{\ln(6^2)}$ , which simplifies to $e^{\ln(36)}$ because $6^2$ equals $36$ .
Apply Property: Apply the property of logarithms and exponents. $\newline$ Using the property $e^{\ln x} = x$ , we can simplify $e^{\ln(36)}$ to just $36$ .