Question
Solve for \( y \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{2 y}=11 \]
Ask by Stephens Medina. in the United States
Mar 14,2025
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Answer
\( y \approx 1.20 \)
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Bonus Knowledge
To solve for \( y \) in the equation \( e^{2y} = 11 \), we start by taking the natural logarithm of both sides. This gives us: \[ 2y = \ln(11) \] Next, divide both sides by 2: \[ y = \frac{\ln(11)}{2} \] Now, let's calculate \( \ln(11) \) using a calculator. The natural logarithm of 11 is approximately 2.397895. Thus, we have: \[ y \approx \frac{2.397895}{2} \approx 1.1989475 \] Rounding this to the nearest hundredth gives: \[ y \approx 1.20 \]