484 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 4.4 Exercises CONCEPT PREVIEW Answer each of the following. 1. For the exponential function ƒ1x2 = ax, where a 71, is the function increasing or decreasing over its entire domain? 2. For the logarithmic function g1x2 = loga x, where a 71, is the function increasing or decreasing over its entire domain? 3. If ƒ1x2 = 6x, what is ƒ -11x2? 4. What is the name given to the exponent to which 4 must be raised to obtain 11? 5. A base e logarithm is called a(n) logarithm, and a base 10 logarithm is called a(n) logarithm. 6. Write log3 12 in terms of natural logarithms using the change-of-base theorem. 7. Why is log2 0 undefined? 8. Between what two consecutive integers must log2 12 lie? 9. The graph of y = log x shows a point on the graph. Write the logarithmic equation associated with that point. 4 8 –1 1 x y (8, 0.90308999) y = log x 0 10. The graph of y = ln x shows a point on the graph. Write the logarithmic equation associated with that point. 2 4 6 8 –1 1 x y y = ln x (2.75, 1.0116009) 0 Find each value. If applicable, give an approximation to four decimal places. See Example 1. 11. log 1012 12. log 107 13. log 0.1 14. log 0.01 15. log 63 16. log 94 17. log 0.0022 18. log 0.0055 19. log 1387 * 232 20. log 1296 * 122 21. log 518 342 22. log 643 287 23. log 387 + log 23 24. log 296 + log 12 25. log 518 - log 342 26. log 643 - log 287 Answer each question. 27. Why is the value of log 1387 * 232 the same as that of log 387 + log 23? 28. Why is the value of log 518 342 the same as that of log 518 - log 342?
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