1. Properties of Logarithms
Section 5.3
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.
Section 5.3
Slide 2

3. 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
Section 5.3
Slide 3

4. Solve the equation Check solution:
Power Property for Logarithms
Solving an Exponential Equation
Example
Solve the equation
Check solution:
Solution
Section 5.3
Slide 4

5. Power Property for Logarithms
Solving an Exponential Equation
Warning
Watch parenthesis:
Section 5.3
Slide 5

6. Power Property for Logarithms
Solving an Exponential Equation
Example
Solve
Solution
Section 5.3
Slide 6

7. Power Property for Logarithms
Solving an Exponential Equation
Solution Continued
Check solution:
Section 5.3
Slide 7