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Chapter 5

Chapter 5. Logarithmic Properties. If a and b are positive numbers and n is rational, then the following properties are true: 1. ln (e) = 1 2. ln (1) = 0 3. ln ( ab ) = ln a + ln b 4. ln ( )= n ln a 5. ln ( )= ln a – ln b. Derivative of an Inverse Function.

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Chapter 5

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  1. Chapter 5

  2. Logarithmic Properties

  3. If a and b are positive numbers and n is rational, then the following properties are true: 1. ln(e) = 1 2. ln(1) = 0 3. ln(ab) = lna + lnb 4. ln( )= nlna 5. ln( )= lna – lnb

  4. Derivative of an Inverse Function

  5. To find the derivative of an inverse function: • Find inverse: Switch x and y • Find derivative: Use implicit differentiation • Solve for y: Use inverse function • Substitute y into derivative

  6. Graphs of inverse functions have reciprocal slopes

  7. Graphs of inverse functions have reciprocal slopes

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