Solve for \( X \) in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ 4^{x+8}=9 \]

To solve the equation \( 4^{x+8} = 9 \), we can start by applying logarithms to both sides. Using the natural logarithm (though any logarithm would work) gives us: \[ \ln(4^{x+8}) = \ln(9) \] Using the property of logarithms that allows us to bring the exponent down, we have: \[ (x + 8) \ln(4) = \ln(9) \] Now, divide both sides by \(\ln(4)\): \[ x + 8 = \frac{\ln(9)}{\ln(4)} \] Next, we isolate \( x \) by subtracting 8 from both sides: \[ x = \frac{\ln(9)}{\ln(4)} - 8 \] Now we can calculate \(\ln(9)\) and \(\ln(4)\): \[ \ln(9) \approx 2.1972, \quad \ln(4) \approx 1.3863 \] Substituting these values in gives us: \[ x = \frac{2.1972}{1.3863} - 8 \] Calculating the fraction: \[ \frac{2.1972}{1.3863} \approx 1.585 \] So now we have: \[ x \approx 1.585 - 8 = -6.415 \] Finally, rounding to the nearest hundredth: \[ \boxed{-6.42} \]