Solve the Logarithm Ratio: Finding log₈(9a)/log₈(3a)

$\frac{\log_89a}{\log_83a}=$

To solve this problem, we'll follow these steps:

• Step 1: Apply the mathematical property using the quotient rule for logarithms.
• Step 2: Simplify the expression into the desired format.

Now, let's work through each step:
Step 1: Given the expression $\frac{\log_8 9a}{\log_8 3a}$, we can directly apply the quotient rule for logarithms, which tells us that $\frac{\log_b M}{\log_b N} = \log_N M$.
Step 2: Applying this formula, we find that $\frac{\log_8 9a}{\log_8 3a} = \log_{3a} 9a$.

Therefore, the solution to the problem is $\log_{3a} 9a$.