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Warm Up: Simplify the Expression. Then State briefly how to simplify the exponents. 1. 2. 3.

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4-5 Properties of Logarithms

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Ex 1: Condense the Expression a. b. Remember that Multiplication and Addition go hand-in-hand. We must have the same base to condense!!! ln is in base e. Division and Subtraction go hand-in-hand.

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Ex 3: Condense the Expression Here, the distributive law can be used.

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Let’s Put it all together… Ex 4&5: Condense the expression.

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We can Also go Backwards! We can also “un-distribute” the exponent Ex6: Expand the expression.

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We can Also go Backwards!! Ex 6&7: Expand the expression.

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Ex 7: Use log 3 ≈.477 and log 2 ≈.301 to approximate the value of the expression

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The Change of Base Formula Let u, b, and c be positive numbers with b≠1 and c≠1. Then: More specifically:

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Ex 8: Use the change of base formula to evaluate the expression

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Ex 1: Use properties of logarithms to evaluate the expression = ? a. b.

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4.5 Apply Properties of Logarithms p. 259 What are the three properties of logs? How do you expand a log? Why? How do you condense a log?

4.5 Apply Properties of Logarithms p. 259 What are the three properties of logs? How do you expand a log? Why? How do you condense a log?

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