A common logarithm has a base of 10. The log key on a calculator finds common logs. Exponential and logarithmic functions can be used to describe quantities that grow or decay continuously over time.

1. A common logarithm has a base of 10. log 5 means log10 5 The log key on your calculator will find common logs.

2. Solve Example 4-3a

3. Solve log 3x = log 17 x log 3 = log 17 x = log 17log 3 1.23040.4771 = = 2.5789 Example 4-3c

4. Solve:

5. Solve: 5x + 3 = 2x+4 log 5x + 3 = log 2x+4 (x + 3) log 5 = (x + 4) log 2 x log 5 + 3 log 5 = x log 2 + 4 log 2 x log 5 – x log 2 = 4 log 2 – 3 log 5 x(log 5 – log 2) = 4 log 2 – 3 log 5 x = 4 log 2 – 3 log 5 log 5 – log 2 = 4(0.3010) – 3(0.6990) 0.6990 – 0.3010 = -2.244

6. Change of base formula

7. Find Example 4-5a

8. Find Example 4-5b

9. Quantities that grow or decay continuously can be described by a natural exponential function. f(x) = ex e is a constant e is approximately 2.71828

10. Use a calculator to evaluate each expression to four decimal places. a. b. Answer:1.3499 Answer:0.1353 Example 5-1c

11. The inverse of the natural exponential function is the natural log function. y = ex loge x = y loge is usually written as ln

12. Use a calculator to evaluate each expression to four decimal places. a. In 2 b. In Answer:0.6931 Answer:–0.6931 Example 5-2f

13. Write as a natural logarithmic equation. x = loge23 x = ln23 Example 5-3a

14. Write as an exponentialequation. loge x = 2.25 Example 5-3c

15. Evaluate Evaluate Evaluate Answer: Answer: Answer: Example 5-4a

16. Solve loge 2x = 0.7 2x = e0.7 x = ½ e0.7 Answer: about 1.0069 Example 5-7d

17. Solve Example 5-5a