7-²log7²

Let's simplify the expression \( 7^{-2} \log 7^2 \).

First, we can break this down step by step:

1. Simplify \( 7^{-2} \): \[ 7^{-2} = \frac{1}{7^2} = \frac{1}{49} \]

2. Simplify \( \log 7^2 \): Using the logarithmic property that \( \log a^b = b \cdot \log a \), \[ \log 7^2 = 2 \cdot \log 7 \]

3. Combine the results: Now, substitute this back into our original expression: \[ 7^{-2} \log 7^2 = \frac{1}{49} \cdot (2 \log 7) = \frac{2 \log 7}{49} \]

Therefore, the simplified expression is: \[ \frac{2 \log 7}{49} \]