Solve for $x$. \[ 6^{-3 x}=5^{-x-4} \] Write the exact answer using either base-10 or base-e logarithms.

Step 1 ：\(\ln(6^{-3x}) = \ln(5^{-x-4})\)

Step 2 ：\(-3x\ln(6) = (-x-4)\ln(5)\)

Step 3 ：\(-3x\ln(6) + x\ln(5) = -4\ln(5)\)

Step 4 ：\(x(-3\ln(6) + \ln(5)) = -4\ln(5)\)

Step 5 ：\(x = \frac{-4\ln(5)}{-3\ln(6) + \ln(5)}\)

Step 6 ：\(\boxed{x = \frac{-4\ln(5)}{-3\ln(6) + \ln(5)}}\)