1. Properties of Logarithms
Section 11.4
Properties of Logarithms

2. For a > 0, b > 0, b ≠ 1, the equations are equivalent.
Exponential/Logarithmic Forms Property
Definition
Introduction
Property
For a > 0, b > 0, b ≠ 1, the equations
are equivalent.

3. Exponential/Logarithmic Forms Property
Solving Equations in Logarithmic Form
Example
Solve for x. 1. 2.
Solution

4. Exponential/Logarithmic Forms Property
Solving Logarithmic Equations in One Variable
Example 1.
Solution

5. Exponential/Logarithmic Forms Property
Solving Logarithmic Equations in One Variable
Solution Continued 2.

6. Power Property for Logarithms
Power Property for Logarithms and of Equality
Property
For x > 0, b > 0 and, b ≠ 1
In words: A logarithm of a power of x is the exponent times the logarithm of x.
For positive real numbers a, b, and c where b ≠ 1, the equations
are equivalent.
Property

7. Solve the equation Check solution:
Power Property for Logarithms
Solving an Exponential Equation
Example
Solve the equation
Check solution:
Solution

8. Power Property for Logarithms
Solving an Exponential Equation
Warning
Watch parenthesis:

9. Power Property for Logarithms
Solving an Exponential Equation
Example
Solve
Solution

10. Power Property for Logarithms
Solving an Exponential Equation
Solution Continued
Check solution:

11. Power Property for Logarithms
Solving an Exponential Equation
Warning
That is why we began by dividing both sides by 3.
To solve some equations of the form abx = c for x, we divide both sides of the equation by a, and then take the log of both sides. Next we use the power property of logarithms.

12. Power Property for Logarithms
Solving an Exponential Equation
Example
Solve
Solution

13. Check solution with graphing calculator:
Power Property for Logarithms
Solving an Exponential Equation
Solution Continued
Check solution with graphing calculator:

14. Power Property for Logarithms
Solving an Exponential Equation
Example
Solve
Solution

15. Solving Equations in One Variable by Using Graphs
Using Graphs to Solve Equations in One Variable
Example
Use a graph to solve
Use the “intersect” feature to find the solution to the
system
Solution