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. An exponential equation is an equation containing one or more expressions that have a variable as an exponent. To solve exponential equations:
Try writing them so that the bases are all the same.
Take the logarithm of both sides.

3. Solving Exponential Equations
Solve the equation.

4. Solving Exponential Equations
Solve the equation.

5. Solving Exponential Equations
Solve the equation.

6. Solving Exponential Equations
Solve the equation.

7. Solving Exponential Equations
Solve the equation.

8. Solving Exponential Equations
Solve the equation.

9. The formula for continuously compounded interest is A = Pert, where A is the total amount, P is the principal, r is the annual interest rate, and t is the time in years.

10. Economics Application
What is the total amount for an investment of $500 invested at 5.25% for 40 years and compounded continuously?
A = Pe rt
Substitute 500 for P, for r, and 40 for t.
A = 500e0.0525(40)
A ≈
Use the ex key on a calculator.
The total amount is $

11. Economics Application
In how many years will it take an investment of $1000 at 6.5% interest compounded continuously to reach $1800?
A = Pe rt
Substitute 1800 for A, 1000 for P, and for r.
1800 = 1000e0.065t
Solve for t.
It will take 9 years to reach $1800.

12. Lesson 9.2 Practice A