Solve for \( y \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{-5 y}=6 \] \( y=\square \)

To solve for \( y \) in the equation \( e^{-5y} = 6 \), we start by taking the natural logarithm of both sides: \[ \ln(e^{-5y}) = \ln(6) \] Using the property of logarithms that allows us to bring the exponent down, we get: \[ -5y = \ln(6) \] Now, divide both sides by \(-5\): \[ y = \frac{\ln(6)}{-5} \] Calculating \( \ln(6) \) using a calculator gives us approximately \( 1.79176 \). So, we have: \[ y = \frac{1.79176}{-5} \approx -0.35835 \] Rounding this to the nearest hundredth, we find: \[ y \approx -0.36 \] So the final answer is: \( y \approx -0.36 \)