1. Properties of Logarithms

2. Properties of Logarithms
Properties are based off of the rules of exponents (since exponents = logs)
The base of the logarithm can not be equal to 1 and the values must all be positive (no negatives in logs)
𝑏=1
𝑏>0

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:
𝑙𝑛 𝑥 = 1 2 ln⁡(𝑥)

6. Pre-Req to Solving Equations:
Simplifying, Expanding, and Condensing.
Let’s try condensing first…

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. Using Properties to Expand Logarithmic Expressions
Use exponential notation
Use the product rule
Use the power rule

11. Now we’ll try expanding…

12. Expand

13. More Properties of Logarithms
This one says if you have an equation, you can take the log of both sides and the equality still holds.
This one says if you have an equation and each side has a log of the same base, you know the "stuff" you are taking the logs of are equal.