7.1.4 Properties of Logarithms − Worksheet
Example 1: Express as a single logarithm. Simplify, if possible. 1. log 5 50 + log 5 62.5 2. log100 + log1000 Example 2: Express as a single logarithm. Simplify, if possible. 4. log 4 320 − log 4 5 5. log5.4 − log0.054
3. log 3 3 + log 3 27
6. log 6 496.8 − log 6 2.3
Example 3: Simplify, if possible. 7. log 8 8 2 Example 4: Simplify, if possible. 11. + log 2 x 2 2 5
8. log
9. log
10.
5
3
log (0.25) 1 2 4
3 3
7 49
12. 2.5 log
13. log
14. log 2 (0.5) 4
19
4 1024
2.5
Example 5: Evaluate. 15. log 1 27 9
16. log 8 32
17. log 5 10
18. log 2 27
Example 6: 19. The Richter magnitude M of an earthquake is related to the energy released in ergs E shown by the formula M E log . = How many times as much energy was released by the 1811 New Madrid, Missouri, earthquake than by the Fort Tejon, California, earthquake? 2 3 10 11.8
Largest Earthquakes in Continental U.S. Location Year M New Madrid, MO 1811 8.1 New Madrid, MO 1812 8.0 Fort Tejon, CA 1957 7.9 San Francisco, CA 1906 7.8 Imperial Valley, CA 1892 7.8
116
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