Question
Find the solution of the exponential equation \( 4 e^{x}=16 \) in terms of logarithms, or correct to four decimal places. \( x= \)
Ask by Hamilton Stewart. in the United States
Mar 13,2025
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Answer
\( x \approx 1.3863 \)
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To solve the equation \( 4 e^{x} = 16 \), first divide both sides by 4: \[ e^{x} = \frac{16}{4} = 4 \] Next, take the natural logarithm of both sides: \[ x = \ln(4) \] Now, using a calculator, you can find that: \[ x \approx 1.3863 \] Thus, \( x \approx 1.3863 \) when rounded to four decimal places.