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Solve. Round your answer to the nearest thousandth. $\newline$ $7 = e^x$ $\newline$ $x =$ ____

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Solve exponential equations using natural logarithms

Full solution

Q. Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

____

Apply ln to both sides: $7 = e^x$ $\newline$ Apply the natural logarithm (ln) to both sides of the equation to solve for x. $\newline$ $\ln(7) = \ln(e^x)$
Simplify using log property: $\ln(7) = \ln(e^x)$ $\newline$ Simplify the equation by using the property of logarithms that allows us to bring the exponent down in front of the log. $\newline$ $\ln(7) = x \cdot \ln(e)$
Simplify further: $\ln(7) = x \cdot \ln(e)$ $\newline$ Since the natural logarithm of $e$ is $1$ ( $\ln(e) = 1$ ), the equation simplifies to: $\newline$ $\ln(7) = x$
Calculate $\ln(7)$ : $\ln(7) = x$ $\newline$ Calculate the natural logarithm of $7$ to find the value of $x$ . $\newline$ $x = \ln(7)$ $\newline$ $x \approx \ln(7) \approx 1.945910149\ldots$
Round to nearest thousandth: $x \approx 1.945910149\ldots$ $\newline$ Round the value of $x$ to the nearest thousandth. $\newline$ $x \approx 1.946$

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