1. 7.3 LOGARITHMIC
FUNCTIONS AS
INVERSES
Part 1: Introduction to Logarithms

2. Logarithms
 The inverse of the exponential function is the
logarithmic function.
 By definition, y = bx is equivalent to logby = x.
 Logarithms exist only for positive real numbers.

3. Logarithms
 The definition of a logarithm can be used to
write exponential functions in logarithmic form:
y = bx is equivalent to logby = x

4. Example:
Write each equation in logarithmic form
100 = 102
y = bx is equivalent to logby = x

5. Example:
Write each equation in logarithmic form
81 = 34
y = bx is equivalent to logby = x

6. Logarithms
To write a logarithmic function in exponential
form, use the definition:
If y = bx is equivalent to logby = x,
then logby = x is equivalent to y = bx

7. Example
Write each equation in exponential form.
log2128 = 7
logby = x is equivalent to y = bx

8. Example
Write each equation in exponential form.
log716,807 = 5
logby = x is equivalent to y = bx

9. Logarithms
 The exponential form of a logarithm can be
used to evaluate a logarithm.
1. Write a logarithmic equation (set the log =
x)
2. Use the definition to write the logarithm in
exponential form
3. Write each side of the equation using the
same base
4. Set the exponents equal to each other
5. Solve

10. Example:
Evaluate each logarithm
log5125

11. Example:
Evaluate each logarithm
log832

12. Example:
Evaluate each logarithm

13. Common Logarithm
 The common logarithm is a logarithm with
base 10
log10
 The common logarithm can be written without a
base, because it is understood to be 10
log10x = log x
 The“log” key on your calculator is the common
logarithm

14. Homework
 P456 #12 – 35