Simplify the Expression: log₉(e²)/log₉(e) Using Log Properties

To solve this problem, we'll simplify the given expression $\frac{\log_9e^2}{\log_9e}$ using logarithmic rules:

Step 1: Apply the power rule of logarithms:
The numerator $\log_9e^2$ can be rewritten using the power rule: $\log_9e^2 = 2 \cdot \log_9e$.

Step 2: Substitute and simplify the fraction:
Substitute the expression from Step 1 into the original problem:
$\frac{\log_9e^2}{\log_9e} = \frac{2 \cdot \log_9e}{\log_9e}$.

Step 3: Cancel common terms:
Since $\log_9e$ appears in both the numerator and the denominator, it cancels out, leaving:
$\frac{2 \cdot \log_9e}{\log_9e} = 2$.

Therefore, the solution to the problem is $\boxed{2}$.