7.1 Review Worksheet (continued)
Write each logarithmic equation in exponential form. 22. log 5 625 = 4 23. log 2 x = 6
24. log 4.5 1 = 0
25. log π π = 1
Evaluate by using mental math. 26. log 2 1
27. log0.001
28. log 4 64
29. log 0.1 100
Use the given x -values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function. 30. f ( x ) 31. f ( x ) = f x x ( ) ; 2, 1,0,1,2,3 x = f x x ( ) ; 2, 1,0,1,2,3 x
=− −
4 5
=− −
4 3
32. The flower color of bigleaf hydrangeas is determined by the soil pH. A gardener growing blue hydrangeas believes that lime may be leaching out of a nearby sidewalk and increasing the pH of the soil. The gardener measures the hydrogen ion concentration and finds it to be 0.0000006 moles per liter. Is the soil still good for growing blue flowers? Explain.
5 < pH < 5.5 5.5 < pH < 6 6 < pH < 6.5
7.1.4 Properties of Logarithms Express as a single logarithm. Simplify, if possible. 33. log 8 4 + log 8 16 34. log2 + log5
35. log 2.5 3.125 + log 2.5 5
36. log1000 − log100
37. log 2 16 − log 2 2
38. log 1.5 6.75 − log 1.5 2
120
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