ofte the following expression in Expanded form \[ \log _{6} \frac{(x-3)^{2}}{(x+3)^{5}} \]

Step 1 ：We are given the expression \(\log _{6} \frac{(x-3)^{2}}{(x+3)^{5}}\)

Step 2 ：We can use the properties of logarithms to expand this expression. The logarithm of a quotient is the difference of the logarithms. The logarithm of a power is the product of the power and the logarithm.

Step 3 ：Applying these properties, we get \(2\log _{6}(x-3) - 5\log _{6}(x+3)\)

Step 4 ：Finally, we simplify the expression to get \(\boxed{\frac{2 \log _{6}(x-3)}{\log(6)} - \frac{5 \log _{6}(x+3)}{\log(6)}}\)