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. \( \log _{4} 48 \)

We can compute logarithms with any base using the change‐of‐base formula:   log₍b₎ a = ln(a) / ln(b). Below are the steps for each logarithm: 13. Find log₅16:   log₅16 = ln(16) / ln(5).   Using a calculator:    ln(16) ≈ 2.773   ln(5) ≈ 1.609   Thus, log₅16 ≈ 2.773 / 1.609 ≈ 1.723. 14. Find log₆82:   log₆82 = ln(82) / ln(6).   Using a calculator:    ln(82) ≈ 4.407   ln(6) ≈ 1.792   Thus, log₆82 ≈ 4.407 / 1.792 ≈ 2.460. 15. Find log₃125:   log₃125 = ln(125) / ln(3).   Note that 125 = 5³ so ln(125) = 3 · ln(5) ≈ 3 × 1.609 = 4.828.   Also, ln(3) ≈ 1.099.   Thus, log₃125 ≈ 4.828 / 1.099 ≈ 4.394. 16. Find log₂100:   log₂100 = ln(100) / ln(2).   Using a calculator:    ln(100) ≈ 4.605   ln(2) ≈ 0.693   Thus, log₂100 ≈ 4.605 / 0.693 ≈ 6.644. 18. Find log₄48:   log₄48 = ln(48) / ln(4).   Using a calculator:    ln(48) ≈ 3.871   ln(4) ≈ 1.386   Thus, log₄48 ≈ 3.871 / 1.386 ≈ 2.795. Rounded to three decimal places, the answers are:   13. 1.723   14. 2.460   15. 4.394   16. 6.644   18. 2.795.