Simplify: log_(4)(x+4)-log_(4)(x-5)

To simplify the expression $log_{4}(x+4)-log_{4}(x-5)$, we can use the properties of logarithms.<br /><br />The property we will use is the quotient rule, which states that the difference of two logarithms with the same base is equal to the logarithm of the quotient of the arguments.<br /><br />Applying the quotient rule, we get:<br /><br />$log_{4}(x+4)-log_{4}(x-5) = log_{4}\left(\frac{x+4}{x-5}\right)$<br /><br />Therefore, the simplified expression is $log_{4}\left(\frac{x+4}{x-5}\right)$.