Solve for \( y \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{y-4}=7 \]

To solve for \( y \) in the equation \( e^{y-4} = 7 \), we start by taking the natural logarithm of both sides: \[ \ln(e^{y-4}) = \ln(7) \] Applying the property of logarithms that states \( \ln(e^x) = x \): \[ y - 4 = \ln(7) \] Now, we isolate \( y \) by adding 4 to both sides: \[ y = \ln(7) + 4 \] Next, we calculate \( \ln(7) \). Using a calculator, we find: \[ \ln(7) \approx 1.945910 \] So we can plug this value back into the equation: \[ y \approx 1.945910 + 4 \approx 5.945910 \] Rounding this to the nearest hundredth: \[ y \approx 5.95 \] Thus, the value of \( y \) rounded to the nearest hundredth is \( \boxed{5.95} \).