Fill in the missing values to make the equations tru (a) \( \log _{8} 7-\log _{8} 3=\log _{8} \square \) (b) \( \log _{2} \square+\log _{2} 11=\log _{2} 55 \) (c) \( -3 \log _{8} 3=\log _{8} \square \)

To solve the missing values in the equations, let's use the properties of logarithms. (a) We use the property that \( \log_a b - \log_a c = \log_a \left( \frac{b}{c} \right) \). Thus, \[ \log _{8} 7 - \log _{8} 3 = \log_{8} \left( \frac{7}{3} \right) \] So the missing value is \( \frac{7}{3} \). (b) We can apply the property \( \log_a b + \log_a c = \log_a (bc) \). This means: \[ \log_{2} \square + \log_{2} 11 = \log_{2} (11 \cdot \square) = \log_{2} 55 \] Thus, \( 11 \cdot \square = 55 \) which gives us \( \square = 5 \). (c) We know that \( n \log_a b = \log_a (b^n) \). This means: \[ -3 \log_{8} 3 = \log_{8} (3^{-3}) = \log_{8} \left( \frac{1}{27} \right) \] So the missing value is \( \frac{1}{27} \).