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Exponential and Logarithmic Equations

- Section 4.4
- Variety of methods of solving exponential

equations - Similar bases
- Logarithm with same base
- Common logs and Natural logs

Model Carbon Dating

- The radioactive element carbon-14 is measured by

a Geiger Counter which counts disintegrations per

minute (dpm). At the time of death the dpm is

15.3. Find the age of a chair leg measuring

10.14 dpm if the model is - Solve

Algebraic Solution Common Base

- Exponential function is 1-1 so
- Thus if bases are the same, then we can set the

powers equal - Example Solve
- Participation Activity Solve
- Can we solve the Carbon Dating Problem using this

method?

Algebraic Solution Inverse Logarithmic Function

- Two logarithmic bases that most technology will

work with - Common Logarithm base 10
- Natural Logarithm base e
- If base of exponential equation is 10 or e, apply

the appropriate logarithmic inverse function

Algebraic Solution

- Solve the Carbon Dating equation
- Isolate the exponential term
- Use the logarithm to bring down the exponent
- Solve the resulting equation
- Will this method work if the base of the exponent

is not 10 or e?

Model Electric Energy

- The demand for electric energy in the U.S. was

800 billion kilowatt hours in 1965. Increase in

demand is predicted to be 8 per year. When will

the demand be 8000? - Model
- Equation

Model Electric Energy

- Solve using natural logarithm
- Can we bring down the power if the base of the

logarithm is not the same as the base of the

exponent?

Logarithmic Power Property

Model Electric Energy

- We can pull down the power even when the base is

not the same - Participation Activity Solve
- Solution

Logarithmic Model

- Humans tend to forget what they have learned. A

psychological experiment determined the percent

of material remembered r after m months is - Determine how many months pass before 60 of the

material is forgotten. - Equation

Logarithmic Equation

- Solve
- Isolate the logarithmic term
- Apply the inverse exponential function to remove

the logarithm - Solution
- Participation Activity Solve
- Solution

Logarithmic Properties

- Solve
- Verify the Logarithmic Sum Property
- Verify the Logarithmic Difference Property

Logarithmic Equation

- Solving logarithmic equations with two

logarithmic terms requires using the sum or

difference Logarithmic Properties - Example
- Solution
- Extraneous solutions are possible, so check them
- Participation Activity Solve

Solving Mixed Equations

- Exponential or logarithmic equations that mix

bases - Equations that mix exponential and logarithmic

expressions - Equations that mix transcendental and algebraic

expressions

Solving Mixed Equations

- Use Graphic Method to solve these mixed equations

(No Transcript)

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