1. Exponential and Logarithmic Functions
1.6
Exponential and Logarithmic Functions

2. Exponentials
Exponential functions occur when a constant (a number) is being raised to a variable power.
Note that this does not necessarily include a constant raised to a transcendental function.
Examples:

3. Properties of Exponents
For positive real numbers a and b, and for real numbers x and y, the following are true:

4. Properties of Exponents
For positive real numbers a and b, and for real numbers x and y, the following are true:

5. Properties of Exponential Functions
The following are true:

6. The number e
Logarithms in base e are called natural logarithms.

7. Natural Logarithms
Let x be a positive, real number.

8. Properties of Natural Logs:
The natural logarithm is an inverse operation to exponentiation with a base of e.
Therefore, the natural log function is the inverse function to the exponential function having base e.

9. Properties of Logarithms
Let x, y, and z be real numbers such that both x and y are non-negative. The following properties are true:

10. Homework
Pg. 54 # 5, 7, 11, 15, 25, 27, 49, 53, 77, 83