Solve for \( x \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{x+9}=15 \]

To solve the equation \( e^{x+9} = 15 \), we start by taking the natural logarithm of both sides: \[ \ln(e^{x+9}) = \ln(15) \] Using the property of logarithms that \( \ln(e^y) = y \), we simplify the left side: \[ x + 9 = \ln(15) \] Next, we isolate \( x \) by subtracting 9 from both sides: \[ x = \ln(15) - 9 \] Now we calculate \( \ln(15) \): Using a calculator, we find that \( \ln(15) \approx 2.70805 \). Now, substituting this value back into the equation: \[ x = 2.70805 - 9 \approx -6.29195 \] Rounding to the nearest hundredth gives us: \[ x \approx -6.29 \] So the final answer is: \[ \boxed{-6.29} \]