Write the expression below as a single logarithm. Assume \( x>8 \). \( \log \left(x^{2}-64\right)-2 \log (x+8) \) \( \log \)

To combine the expression into a single logarithm, we start by using the properties of logarithms. The term \(2 \log (x+8)\) can be rewritten using the power rule: \[ 2 \log (x+8) = \log((x+8)^2) \] So the original expression becomes: \[ \log \left(x^{2}-64\right) - \log((x+8)^2) \] Next, we apply the quotient rule of logarithms, which allows us to subtract logs: \[ \log \left(\frac{x^{2}-64}{(x+8)^2}\right) \] Now we can simplify \(x^2 - 64\) as it factors to \((x-8)(x+8)\): \[ \log \left(\frac{(x-8)(x+8)}{(x+8)^2}\right) \] This simplifies to: \[ \log \left(\frac{x-8}{x+8}\right) \] So, the final expression as a single logarithm is: \[ \log \left(\frac{x-8}{x+8}\right) \]