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What is the natural logarithm of $\ln(e^{2x})$ ?

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Evaluate integers raised to positive rational exponents

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Q. What is the natural logarithm of

\ln(e^{2x})

?

Recognize Properties: Recognize the properties of logarithms and exponents. $\newline$ The natural logarithm function $\ln(x)$ is the inverse of the exponential function $e^x$ . Therefore, $\ln(e^x) = x$ for any $x$ .
Apply Property: Apply the property to the given expression. $\newline$ Since $\ln(e^{2x})$ involves the natural logarithm of an exponential function with the same base ( $e$ ), we can simplify it directly using the property from Step $1$ . $\newline$ $\ln(e^{2x}) = 2x$

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