(8.) \( \log _{4} x-\log _{4} 8=3 \)

Let's first combine the logarithmic terms using the property of logarithms: \[ \log _{4} x - \log _{4} 8 = \log_{4} \left(\frac{x}{8}\right) \] Now, we can rewrite the original equation as follows: \[ \log_{4} \left(\frac{x}{8}\right) = 3 \] To eliminate the logarithm, we can exponentiate both sides with base 4: \[ \frac{x}{8} = 4^3 \] Calculating \(4^3\): \[ 4^3 = 64 \] Now we have: \[ \frac{x}{8} = 64 \] To solve for \(x\), we multiply both sides by 8: \[ x = 64 \cdot 8 = 512 \] Thus, the solution is: \[ \boxed{512} \]