Evaluate \( \log _{4} 16 \) without a calculator. Note: If your answer is a fraction, enter your answer as a reduced improper fraction. Ex. \( 4 / 3 \) for \( \frac{4}{3} \). type your answer...

To evaluate \( \log_{4} 16 \), we start by rewriting 16 as a power of 4. We know that \( 4 = 4^1 \) and \( 16 = 4^2 \). Therefore, we can express 16 in terms of base 4: \[ 16 = 4^2 \] Now we can use the property of logarithms: \[ \log_{b} (a^c) = c \cdot \log_{b} a \] Thus, we can substitute: \[ \log_{4} 16 = \log_{4} (4^2) = 2 \cdot \log_{4} 4 \] Since \( \log_{4} 4 = 1 \), we have: \[ \log_{4} 16 = 2 \cdot 1 = 2 \] The final answer is: \[ \boxed{2} \]