Score: 4.86/8 Answered: 7/8 Question 8 Simplify. Enter the result as a single logarithm with a coefficient of 1. log_(8)(6x)-log_(8)(7x^7)=square

To simplify the expression \(\log_{8}(6x) - \log_{8}(7x^{7})\), we can use the properties of logarithms. Specifically, we will use the quotient rule for logarithms, which states: Applying this property to the given expression: Next, we simplify the fraction inside the logarithm: So the expression becomes: Using the product rule for logarithms, which states \(\log_b(ab) = \log_b(a) + \log_b(b)\), we can further simplify: Since \(\log_{8}(x^{-6}) = -6 \log_{8}(x)\), we have: Thus, the simplified form of the original expression is: