Deriving and Integrating Logarithms and Exponential Equations

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Presentation transcript:

Deriving and Integrating Logarithms and Exponential Equations AP Calculus AB

Logarithmic form: Exponential form: Loga b = c can be written as: ac = b

What is a Logarithm? Logarithmic Exponential Log3 81 = x 3x = 81 In calculator, we can do the change of base formula in logarithmic form: Log 81 3x = 81 Log 3 = 4 34 = 81 3x = 34 x = 4

Theorem 5.13 Derivatives for Bases Other Than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Examples for Derivatives for Bases other than e

Differentiate. Hint: Take the ln of both sides.

Logarithmic form: Exponential form: Loga b = c can be written as: ac = b