4.4.ppt - Exponential and Logarithmic Equations Section 4.4 OBJECTIVES Learn how to \u2022 Use like bases to solve exponential equations \u2022 Use logarithms

4.4.ppt - Exponential and Logarithmic Equations Section 4.4...

This preview shows page 1 - 10 out of 25 pages.

Exponential and Logarithmic Equations Section 4.4
Image of page 1
OBJECTIVES Learn how to Use like bases to solve exponential equations Use logarithms to solve exponential equations Use the definition of a logarithm to solve logarithmic equations Use one to one property of logarithms to solve logarithmic equations Solve applied problems involving exponential and logarithmic equations
Image of page 2
Properties used to solve Exponential and Logarithmic Equations One to one properties a x = a y if, and only if x=y log a x = log a y if, and only if x = y. Inverse properties: log a a x = x x a x a log
Image of page 3
Exponential Equation Method I This mehod based on “One to One Property”: b M = b N if, and only if M = N Write each side as a power of the same base Then set exponents = and solve.
Image of page 4
Image of page 5
Example:Solve 27x+3= 9x-1
Image of page 6
Example: Solve 27 x+3 = 9 x-1 Solution: 3 3x+9 = 3 2x-2 Now we can set the exponents = since bases are equal: 3x +9 = 2x -2 Sub 2x and 9 both sides x = -11
Image of page 7
Solve Exponential Equations Using Natural Logarithms 1. Isolate the exponential expression on one side 2. Take natural logarithm of both sides of equation 3. Simplify using properties like ln b x = x ln b or ln e x = x 4. Solve for the variable
Image of page 8
Example Solve for x: 40e .6x -3 = 237
Image of page 9
Image of page 10

You've reached the end of your free preview.

Want to read all 25 pages?

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture