Solve for $$ y $$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $$ e^{2 y}=11 $$

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UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   e^{2y} = 11
   $$

2. Take the natural logarithm on both sides to eliminate the exponential:
   $$
   \ln(e^{2y}) = \ln(11)
   $$

3. Use the logarithm power rule $$\ln(e^{2y}) = 2y$$:
   $$
   2y = \ln(11)
   $$

4. Solve for $$ y $$ by dividing both sides by 2:
   $$
   y = \frac{\ln(11)}{2}
   $$

5. Use a calculator to compute $$\ln(11)$$ (without rounding intermediate steps):
   $$
   \ln(11) \approx 2.397895273
   $$
   Thus,
   $$
   y \approx \frac{2.397895273}{2} \approx 1.198947637
   $$

6. Round the result to the nearest hundredth:
   $$
   y \approx 1.20
   $$
$$ y \approx 1.20 $$

Solve for \( y \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{2 y}=11 \]

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