1. Ch 3.3: Properties of Logarithms
Change of Base Formulas
Use when solving exponential form does not appear to give integer answers
Base b
Base 10
Base e
Ex: Find OR

2. Other Useful properties: **All hold for the nature log (ln) as well**
Ex: Write each logarithm in terms of ln2 and ln3
1. Rewrite 6
as 3٠2
1.Property 2
2.Property 1
2.Rewrite 27 as 33
3.Property 3

3. More examples Expand using the properties of logarithms 1. Property 1
2. Change radical
to fraction exponent
3. Property 3

4. More examples Condense using the properties of logarithms
1. Property 3
2. Rewrite as radical
3. Property 1
1. Property 3
2. Property 2

5. Application
Students taking the SAT Math test on average improve each time by the model
where 1 ≤ t ≤ 4.
What is the average score after taking the test for the 3rd time?
1. Substitute in 3
2. Property 3
3. Change of base
4. Divide and simplify