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##### Logarithms

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**Logarithms**Math 3 Standard MM3A3**Background:**• Before there were calculators that could evaluate powers, mathematicians had to use logarithms • Logarithms are helpful especially when there are non-integer powers • For example:**Definition:**• The logarithm of x with base a • is denoted as: • This is read “log base a of x” • and defined as:**Logarithmic form:**Exponential form: Translate from logarithmic form to exponential form:**Logarithmic form:**Exponential form: Translate from exponential form to logarithmic form:**Special Logarithms**because because because**Properties of Logarithms**Math 3 MM3A2**The Product Property**• Example:**The Quotient Property**• Example:**The Power Property**• Example:**Expansion**• The properties are used to expand the logarithm • Each factor will have it’s own log • Example: Expand each logarithm**Expansion**• Example: Expand each logarithm**You Try!**• Expand the following logarithms using the properties of logarithms:**Condense**• The properties are used to condense the logarithm • There will be one single log • Example: Condense each logarithm**Condense**• Example: Condense each logarithm**You Try!**• Condense the following logarithms in to a single logarithm using the properties of logarithms: