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Logarithms Logarithmic and Exponential Form

This instructional aid was prepared by the Tallahassee Community College Learning Commons. Logarithms A logarithm of a given number , is the exponent required for the base , to be raised to in order to produce that number . log = = Note that means " " Logarithmic and Exponential Form Change logarithm equations to Exponential form or Exponential equations to Logarithmic form using the definition of a logarithm. Example: Given 432 =8 , change the equation to Logarithmic form. Solution: Compare the equation to the definition and rewrite it. Definition: log = = Given: 432 =8 Notice that =4, =8,and =32,respectively. Therefore, using the definition: 432 =8 = Example: Given log255=12 , change the equation to Exponential form.

Solving Logarithm and Exponential Equations Evaluate logarithmic equations by using the definition of a logarithm to change the equation into a form that can then be solved. Example: Given 3 −1=7 , solve for . Solution: Step 1: Set up the equation and use the definition to change it.

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