1. Exponential and Logarithmic Equations
Honors Precalculus
November 1/2, 2016
Mr. Agnew

2. Essential Question Essential Vocabulary
How do you solve logarithmic and exponential equations?
Essential Vocabulary
Exponential Equation
Logarithmic Equation
Laws of Logarithms
Change of Base Formula

3. Change of Base Formula 𝒍𝒐𝒈 𝒃 𝑴= 𝒍𝒐𝒈𝑴 𝒍𝒐𝒈𝒃
Our calculators only understand the two special logarithms (common and natural)
To evaluate logarithms with a base other than 10 or e on the calculator, we use the change of base formula:
𝒍𝒐𝒈 𝒃 𝑴= 𝒍𝒐𝒈𝑴 𝒍𝒐𝒈𝒃

4. Solving Exponential Equations
An exponential equation is an equation in which the variable is in the exponent.
How do we remove a variable from the exponent?
𝒚= 𝒃 𝒙 → 𝒍𝒐𝒈 𝒃 𝒚=𝒙
We rewrite it as a logarithm.

5. Solving Exponential Equations
Steps to solve exponential equations:
Isolate term that contains exponent
Convert to logarithmic form
Use change of base formula if necessary
Solve for variable
Examples

6. Logarithmic Equations
A logarithmic equation is an equation in which the variable is “behind” the logarithm.
𝒍𝒐𝒈 𝒃 𝒚=𝒙→𝒚= 𝒃 𝒙
Remember how to rewrite from logarithmic to exponential form:

7. Logarithmic Equations
Solving logarithmic equations:
Combine all logarithmic expressions
Isolate logarithm
Rewrite in exponential form
Solve for variable
Examples…

8. Solving Equations Graphically
How have we used the calculator to solve equations before?
Set equation equal to zero, graph, and find zeros.
Guided Practice

9. Homework:
page 315 – 316 #11 – 25 (Odd), 26, 30, 31, 39, 49, 50