Solve for $x$
\[
16^{6 x}=11^{-x-3}
\]

Write the exact answer using either base-10 or base- $e$ logarithms.
\[
x=
\]

Answer

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Answer

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

Steps

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 $x = \boxed{-\log\left(\frac{11^3}{16^6}\right)}$.