Solve for $x$ \[ 16^{6 x}=11^{-x-3} \] Write the exact answer using either base-10 or base- $e$ logarithms. \[ x= \]

Step 1 ：Given the equation \(16^{6x} = 11^{-x-3}\), we can take the natural logarithm of both sides to get \(\ln(16^{6x}) = \ln(11^{-x-3})\).

Step 2 ：Simplifying the equation gives \(6x \cdot \ln(16) = (-x-3) \cdot \ln(11)\).

Step 3 ：Solving for x, we get \(x = -\log\left(\frac{11^3}{16^6}\right)\).

Step 4 ：So, the final answer is \(x = \boxed{-\log\left(\frac{11^3}{16^6}\right)}\).