Fill in the missing values to make the equations true. \[ \begin{array}{l}\text { (a) } \log _{7} 4+\log _{7} 3=\log _{7} \square \\ \text { (b) } \log _{3} \square-\log _{3} 7=\log _{3} \frac{5}{7} \\ \text { (c) } \log _{3} 4=2 \log _{3} \square\end{array} \]

To solve for the missing values in the given logarithmic equations, we can use the properties of logarithms. (a) Using the property of logarithms that states \(\log_a b + \log_a c = \log_a (b \cdot c)\): \[ \log_{7} 4 + \log_{7} 3 = \log_{7} (4 \cdot 3) \] Calculating \(4 \cdot 3\), we get 12. Thus: \[ \log_{7} 4 + \log_{7} 3 = \log_{7} 12 \] So, the missing value for (a) is **12**. (b) Using the property of logarithms that states \(\log_a b - \log_a c = \log_a \left( \frac{b}{c} \right)\): \[ \log_{3} \square - \log_{3} 7 = \log_{3} \frac{5}{7} \] This can be rewritten as: \[ \log_{3} \left( \frac{\square}{7} \right) = \log_{3} \frac{5}{7} \] Since the logarithms are equal, we can set the arguments equal to each other: \[ \frac{\square}{7} = \frac{5}{7} \] Multiplying both sides by 7 gives us \(\square = 5\). So, the missing value for (b) is **5**. (c) Using the property of logarithms that states \(k \log_a b = \log_a (b^k)\): \[ \log_{3} 4 = 2 \log_{3} \square \implies \log_{3} 4 = \log_{3} (\square^2) \] Since the logarithms are equal, we can set the arguments equal to each other: \[ 4 = \square^2 \] Taking the square root gives us: \[ \square = \sqrt{4} = 2 \] So, the missing value for (c) is **2**. In summary, the missing values are: - (a) 12 - (b) 5 - (c) 2