1. 8.4 – Properties of Logarithms

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. Product Rule logbMN = LogbM + logbN Ex: logbxy = logbx + logby
Ex: log6 = log 2 + log 3
Ex: log39b =
log39 + log3b

4. Quotient Rule
Ex:

5. Power Rule
Ex:

6. Change of Base Rule

7. Let’s try some
Working backwards now: write the following as a single logarithm.

8. Let’s try some
Write the following as a single logarithm.

9. Let’s try something more complicated . . .
Condense the logs
log 5 + log x – log 3 + 4log 5

10. Let’s try something more complicated . . .
Condense the logs
log 5 + log x – log 3 + 4log 5

11. Let’s try something more complicated . . .
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12. Let’s try something more complicated . . .
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