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

Answer

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Answer

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

Steps

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