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**Laws (Properties) of Logarithms**

Section 3.3

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Objectives Rewrite (expand) a logarithm to contain no logarithms of products, quotients, or powers. Rewrite (condense) a logarithmic expression into the logarithm of a single value. Use the change of base formula to rewrite a logarithm as a common logarithm or a natural logarithm.

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**Vocabulary product rule: multiplication becomes addition**

quotient rule: division becomes subtraction power rule: exponent becomes multiplier

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**Laws of Logarithms product rule - multiplication becomes addition**

quotient rule - division becomes subtraction power rule - exponent becomes multiplier

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Change of Base Formula

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Use the Laws of Logarithms to rewrite the expression in a form with no logarithm of a product, quotient or power.

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Use the Laws of Logarithms to rewrite the expression in a form with no logarithm of a product, quotient or power.

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**Rewrite the expression as a single logarithm.**

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**Rewrite the expression as a single logarithm.**

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**Evaluate the expression without using the Change of Base Formula.**

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**Evaluate the expression using the Change of Base Formula**

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