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8.4 Properties of Logarithms

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**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

**4. **Quotient Rule
Ex:
Ex:
Ex:

**5. **Power Rule
Ex:
Ex:
Ex:

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

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

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

**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 . . . Expand

**11. **Let’s try something more complicated . . . Expand