Solve for x, rounding to the nearest hundredth. e^(x)=4 Answer:

Write Equation: Write down the equation that needs to be solved. We have the equation e^(x) = 4.Apply Natural Logarithm: Apply the natural logarithm (ln) to both sides of the equation to solve for x. Taking the natural logarithm of both sides, we get ln(e^(x)) = ln(4).Simplify Left Side: Simplify the left side of the equation using the property that ln(e^(x)) = x. This simplifies to x = ln(4).Calculate ln(4): Calculate the value of ln(4) using a calculator. Using a calculator, we find that ln(4) ≈ 1.386294361.Round to Nearest Hundredth: Round the result to the nearest hundredth. Rounding 1.386294361 to the nearest hundredth gives us x ≈ 1.39.

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Solve for
x, rounding to the nearest hundredth.

e^(x)=4
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $e^{x}=4$ $\newline$ Answer:

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Precalculus

Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

e^{x}=4

\newline

Answer:

Write Equation: Write down the equation that needs to be solved. $\newline$ We have the equation $e^{x} = 4$ .
Apply Natural Logarithm: Apply the natural logarithm ( $\ln$ ) to both sides of the equation to solve for $x$ . $\newline$ Taking the natural logarithm of both sides, we get $\ln(e^{x}) = \ln(4)$ .
Simplify Left Side: Simplify the left side of the equation using the property that $\ln(e^{x}) = x$ . This simplifies to $x = \ln(4)$ .
Calculate $\ln(4)$ : Calculate the value of $\ln(4)$ using a calculator. $\newline$ Using a calculator, we find that $\ln(4) \approx 1.386294361$ .
Round to Nearest Hundredth: Round the result to the nearest hundredth. $\newline$ Rounding $1.386294361$ to the nearest hundredth gives us $x \approx 1.39$ .