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Solve for
x, rounding to the nearest hundredth.

38e^(x)=304
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $38 e^{x}=304$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

38 e^{x}=304

\newline

Answer:

Write Equation: Write down the given equation. $\newline$ We are given the equation $38e^{x} = 304$ . We need to solve for $x$ .
Divide and Calculate: Divide both sides of the equation by $38$ to isolate $e^{x}$ . $\newline$ $e^{x} = \frac{304}{38}$ $\newline$ Calculate the right side of the equation. $\newline$ $e^{x} = 8$
Apply Natural Logarithm: Apply the natural logarithm ( $\ln$ ) to both sides of the equation to solve for $x$ . $\ln(e^{x}) = \ln(8)$ Use the property of logarithms that $\ln(e^{x}) = x$ . $x = \ln(8)$
Calculate $x$ : Calculate the value of $x$ using a calculator. $x = \ln(8)$ $x \approx 2.0794415416798357$ Round the answer to the nearest hundredth. $x \approx 2.08$

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