Solve for $$ y $$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $$ e^{y+5}=4 $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation:
   $$
   e^{y+5}=4
   $$

2. Take the natural logarithm of both sides:
   $$
   \ln\left(e^{y+5}\right)=\ln(4)
   $$

3. Use the logarithmic property $$\ln\left(e^x\right)=x$$:
   $$
   y+5=\ln(4)
   $$

4. Solve for $$ y $$ by subtracting 5 from both sides:
   $$
   y=\ln(4)-5
   $$

5. Compute $$\ln(4)$$ (unrounded intermediate result):
   $$
   \ln(4) \approx 1.38629436112
   $$

6. Substitute the value into the expression for $$ y $$:
   $$
   y \approx 1.38629436112-5 \approx -3.61370563888
   $$

7. Round the final answer to the nearest hundredth:
   $$
   y \approx -3.61
   $$
$$ y \approx -3.61 $$

Solve for in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.