Notes 4­3 Logarithmic Functions
Objectives:
­ Write equivalent forms for exponential and logarithmic functions
­ Write, evaluate, and graph logarithmic functions
Why learn this?
A logarithmic scale is used to measure the acidity, or pH, of water. 1
How many times would you have to double $1 before you had $8?
How many times would you have to double a $1 to have $512?
You could solve this by using the inverse operation that undoes raising a base to an exponent. This operation is called finding the logarithm.
2
A logarithm is the exponent to which a specified base is raised to obtain a certain a given value. 3
Ex. Write each exponential equation in logarithmic form.
a.
b.
c.
d.
e. 4
Try These:
Ex. Write each exponential equation in logarithmic form. a.
b.
c. 5
Ex. Write each logarithmic equation in exponential form.
a.
b.
c.
d.
e.
6
Try These:
Ex. Write each logarithmic equation in exponential form.
a.
b.
c.
7
A logarithm with base 10 is called a common logarithm. If no base is written for a logarithm, the base is assumed to be 10.
ex. 8
Ex. Evaluate by using mental math.
a.
b. 9
Try These:
Ex. Evaluate using mental math. a.
b. 10
Because logarithms are the inverses of exponents, the inverse of an exponential function is a logarithmic function.
** Notice that the domain and range of each function are switched. 11
Ex. Use the given x­values to graph each function. Then graph its inverse. Describe the domain and range of the inverse function.
a. 12
b. 13
Try These:
Ex. Use the given x­values to graph the function. Then graph its inverse. Describe the domain and range of the inverse function. 14
The table list hydrogen ions concentrations for a number of food items. Find the pH of each.
(pH = ­ log [H+])
a. Milk
b. Tomatoes
c. Lemon Juice
15