Find the value of each logarithm to three decimal places. 13. \( \log _{5} 16 \) 14. \( \log _{6} 82 \) 15. \( \log _{3} 125 \) 16. \( \log _{2} 100 \) 18. \( \log _{4} 48 \)

To find the logarithmic values, we'll use the change of base formula, which states that \( \log_{b}(a) = \frac{\log_{k}(a)}{\log_{k}(b)} \) for any positive base \( k \). Commonly, we use base 10 or base e (natural logarithm). 13. \( \log_{5}(16) \approx \frac{\log_{10}(16)}{\log_{10}(5)} \approx 1.722 \) 14. \( \log_{6}(82) \approx \frac{\log_{10}(82)}{\log_{10}(6)} \approx 2.290 \) 15. \( \log_{3}(125) \approx \frac{\log_{10}(125)}{\log_{10}(3)} \approx 4.464 \) 16. \( \log_{2}(100) \approx \frac{\log_{10}(100)}{\log_{10}(2)} \approx 6.644 \) 18. \( \log_{4}(48) \approx \frac{\log_{10}(48)}{\log_{10}(4)} \approx 3.584 \) Here are the answers rounded to three decimal places: - \( \log_{5}(16) \approx 1.722 \) - \( \log_{6}(82) \approx 2.290 \) - \( \log_{3}(125) \approx 4.464 \) - \( \log_{2}(100) \approx 6.644 \) - \( \log_{4}(48) \approx 3.584 \)