1
MA 15200
Lesson 31, Section 4.4
An
exponential equation
is an equation with a variable in one of its exponents.
A
logarithmic equation
is an equation with one or more logarithmic expressions that
contain a variable.
Solving an exponential equations:
(There are 2 types of exponential equations.)
A
If you can write the left and right sides using the same base, then the exponents
are the same.
For example:
(
)
(
)
3
5
1
3
5
1
3
4
9
4(5
1)
8
16
2
2
2
2
9
20
4
4
11
4
11
x
x
x
x
x
x
x
x
x
x



=
=
=
=

=
=
This cannot always be done, however.
If two quantities are equal, the logs to the same base of those quantities are equal.
Therefore:
log
log
b
b
M
N
M
N
=
⇔
=
B
Therefore, to solve an exponential equation:
1.
Write with exponential expression on one side.
2.
Take either the common logs or the natural logs of both sides.
3.
Use the properties of logs and solve.
4.
Use a scientific calculator if asked to approximate.
Ex 1:
Solve each equation.
Approximate to 4 decimal places, if necessary.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 Equations, Exponents, Natural logarithm, Logarithm, exponential equation

Click to edit the document details