Ch 3.3: Properties of Logarithms

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Presentation transcript:

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

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

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

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

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