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8.4 properties of logarithms

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8.4 properties of logarithms

1. 1. LOGARITHMIC PROPERTY DAY!!!! 8.4 – Properties of Logarithms
2. 2. Properties of Logarithms  There are four basic properties of logarithms that we will be working with. For every case, the base of the logarithm can not be equal to 1 and the values must all be positive (no negatives in logs)
3. 3. Product Rule logbMN = LogbM + logbN  Ex: logbxy = logbx + logby  Ex: log6 = log 2 + log 3  Ex: log39b = log39 + log3b
4. 4. Quotient Rule log    Ex: log Ex: log Ex: log M b 5 MN 2 P M log 5 x log log 2 a log y a 2 b N x 5 log log 2 M log b N y 5 2 5 log 2 N log 2 P
5. 5. Power Rule log  Ex: log  Ex:  Ex: log 5 log 2 B 2 5 x 3 7 M b a b 4 x x log 2 log x log 3 log 5 b M B 2 5 7 a 4 log 7 b
6. 6. Let’s try some  Working backwards now: write the following as a single logarithm. log 4 4 log 4 16 log 5 log 2 2 log 2 m 4 log 2 n
7. 7. Let’s try some  Write the following as a single logarithm. log 4 4 log 4 16 log 5 log 2 2 log 2 m 4 log 2 n
8. 8. Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5 log 4 5 2 log 4 x 5 (log 4 3 x log 4 5 x )
9. 9. Let’s try something more complicated . . . Condense the logs log 5 + log x – log 3 + 4log 5 log 4 5 2 log 4 x 5 (log 4 3 x log 4 5 x )
10. 10. Let’s try something more complicated . . .  Expand log 10 x 3y 3 4 2 log 2 x 8 5
11. 11. Let’s try something more complicated . . .  Expand log 10 x 3y 3 4 2 log 2 x 8 5