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

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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 2.Property 1 1.Property 2 2.Rewrite 27 as 3 3 3.Property 3

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

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

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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

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Log Properties. Because logs are REALLY exponents they have similar properties to exponents. Recall that when we MULTIPLY like bases we ADD the exponents.

Log Properties. Because logs are REALLY exponents they have similar properties to exponents. Recall that when we MULTIPLY like bases we ADD the exponents.

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