477 4.4 Evaluating Logarithms and the Change-of-Base Theorem For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so. 15. ƒ1x2 = 3x - 6 16. ƒ1x2 = 21x + 123 17. ƒ1x2 = 3x2 18. ƒ1x2 = 2x - 1 5 - 3x 19. ƒ1x2 = 23 5 - x4 20. ƒ1x2 = 2x2 - 9, x Ú 3 Write an equivalent statement in logarithmic form. 21. a 1 10b -3 = 1000 22. ab = c 23. A 23 B 4 = 9 24. 4-3/2 = 1 8 25. 2x = 32 26. 274/3 = 81 Solve each equation. 27. 3x = 7log7 6 28. x = log 10 0.001 29. x = log6 1 216 30. logx 5 = 1 2 31. log10 0.01 = x 32. logx 3 = -1 33. logx 1 = 0 34. x = log228 35. logx2 3 5 = 1 3 36. log1/3 x = -5 37. log10 1log2 2102 = x 38. x = log 4/5 25 16 39. 2x - 1 = log6 6x 40. x = Blog 1/2 1 16 41. 2x = log 2 16 42. log3 x = -2 43. a 1 3b x+1 = 9x 44. 52x-6 = 25x-3 4.4 Evaluating Logarithms and the Change-of-Base Theorem ■ Common Logarithms ■ Applications and Models with Common Logarithms ■ Natural Logarithms ■ Applications and Models with Natural Logarithms ■ Logarithms with Other Bases Common Logarithms Two of the most important bases for logarithms are 10 and e. Base 10 logarithms are common logarithms. The common logarithm of x is written log x, where the base is understood to be 10. Common Logarithm For all positive numbers x, log x =log10 x. A calculator with a log key can be used to find the base 10 logarithm of any positive number.
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