1. How do we solve exponential and logarithmic equations and equalities?
Exponential and Logarithmic Equations and Inequalities
Essential Questions
How do we solve exponential and logarithmic equations and equalities?
How do we solve problems involving exponential and logarithmic equations?
Holt McDougal Algebra 2
Holt Algebra 2

2. Equations with logarithms on both sides of the equal sign.
A logarithmic equation is an equation with a logarithmic expression that contains a variable. There are two kinds of logarithmic equations:
Equations with logarithms on both sides of the equal sign.
Equations with logarithms only on one side. (exponentiate the equation)
Check answer to make sure it does not give a log(x < 0).

3. Solving Logarithmic Equations
Solve the equation.

4. Solving Logarithmic Equations
Solve the equation.

5. Solving Logarithmic Equations
Solve the equation.

6. Solving Logarithmic Equations
Solve the equation.

7. Solving Logarithmic Equations
Solve the equation.

8. Solving Logarithmic Equations
Solve the equation.

9. Solving Logarithmic Equations
Solve the equation.

10. Solving Logarithmic Equations
Solve the equation.

11. Solving Logarithmic Equations
Solve the equation.

12. Economics Application
The moment magnitude M of an earthquake that releases energy E (in ergs) can be modeled by this equation:
On October 9, 1984, the largest earthquake in Georgia occurred in Dalton with a magnitude of 4.2. How much energy did this earthquake release?
4.2 = 0.219ln E +1.17
Substitute 4.2 for M.
Solve for E.
The earthquake released about 1,020,309 ergs of energy.

13. Lesson 9.2 Practice B