1. Logarithmic Functions
Section 3.2A
Logarithmic Functions
Logarithmic functions are functions in which the logarithm of a variable is present.
For x > 0, a > 0, and a ≠ 1,
y = loga x if and only if x = a y.
The function given by f (x) = loga x is called the logarithmic function with base a.

2. Ex 1: Use the definition of logarithmic function to
Ex 1: Use the definition of logarithmic function to evaluate each logarithm at the indicated value of x.
a. f (x) = log2 x, x = 32
b. f (x) = log3 x, x = 1
c. f (x) = log4 x, x = 2
d. f (x) = log10 x, x =
f (x) = 5
f (x) = 0
f (x) = 0.5
f (x) = -2
Note: log x means log10 x and is called the common logarithm.

3. Ex 2: Use a calculator to evaluate the function
f (x) = log x at each value of x.
a. x = 10
b. x = 2.5
c. x = -2
d. x = 0.25
f (x) = 1
f (x) =
Not possible

4. Properties of Logarithms

5. Ex 3: Using the properties of logarithms:
a. Solve for x: loga x = loga 3
b. Solve for x: log4 4 = x
c. Simplify: log5 58
d. Simplify: 7log714
x = 3
x = 1 8 14

6. Ex 4: On the same coordinate plane, sketch the graph of each function
a. f (x) = 2x b. g (x) = log2 x

7. Suggested Assignment:
S 3.2A pg 195 #1 – 34