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# Alg2 lesson 10-4 and 10-5

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### Alg2 lesson 10-4 and 10-5

1. 1. A common logarithm has a base of 10. log 5 means log10 5The log key on your calculator will findcommon logs.
2. 2. Solve
3. 3. Solve log 3x = log 17 x log 3 = log 17 log 17 x = log 3 1.2304 = 0.4771 = 2.5789
4. 4. Solve:
5. 5. Solve: 5x + 3 = 2x + 4log 5x + 3 = log 2x + 4(x + 3) log 5 = (x + 4) log 2x log 5 + 3 log 5 = x log 2 + 4 log 2x log 5 – x log 2 = 4 log 2 – 3 log 5x(log 5 – log 2) = 4 log 2 – 3 log 5x = 4 log 2 – 3 log 5 = 4(0.3010) – 3(0.6990) log 5 – log 2 0.6990 – 0.3010 = -2.244
6. 6. Change of base formula
7. 7. Find
8. 8. Find
9. 9. Quantities that grow or decaycontinuously can be described by anatural exponential function. f(x) = ex e is a constant e is approximately 2.71828
10. 10. Use a calculator to evaluate each expression to fourdecimal places.a. Answer: 1.3499b. Answer: 0.1353
11. 11. The inverse of the natural exponentialfunction is the natural log function. y = ex loge y = x loge is usually written as ln
12. 12. Use a calculator to evaluate each expression tofour decimal places.a. In 2 Answer: 0.6931b. In Answer: –0.6931
13. 13. Write as a natural logarithmic equation. x = loge 23 x = ln 23
14. 14. Write as an exponential equation. loge x = 2.25