Use properties of logarithms to evaluate the expression. \( 2 \log 5+\log 4 \) \( \square \)

To evaluate the expression \( 2 \log 5 + \log 4 \), we can first use the power rule of logarithms, which states that \( a \log b = \log b^a \). This allows us to rewrite \( 2 \log 5 \) as \( \log 5^2 \), which is \( \log 25 \). Now, our expression becomes: \[ \log 25 + \log 4 \] Next, we can use the product rule of logarithms, which states that \( \log a + \log b = \log (a \cdot b) \). Therefore, we can combine our logs: \[ \log 25 + \log 4 = \log (25 \cdot 4) \] Calculating \( 25 \cdot 4 \), we get \( 100 \). Hence, we have: \[ \log (25 \cdot 4) = \log 100 \] We know that \( \log 100 = \log 10^2 = 2 \), thus: \[ 2 \log 5 + \log 4 = 2 \] So the final evaluated expression is: \[ \boxed{2} \]