4.4.ppt - Exponential and Logarithmic Equations Section 4.4...

Exponential and
Logarithmic Equations
Section 4.4

OBJECTIVES
Learn how to
•
Use like bases to solve exponential equations
•
Use logarithms to solve exponential equations
•
Use the definition of a logarithm to solve
logarithmic equations
•
Use one to one property of logarithms to solve
logarithmic equations
•
Solve applied problems involving exponential
and logarithmic equations

Properties used to solve Exponential
and Logarithmic Equations
•
One to one properties
a
x
= a
y
if, and only if x=y
log
a
x = log
a
y if, and only if x = y.
•
Inverse properties:
log
a
a
x
= x
x a
x
a

log

Exponential Equation Method I
This mehod based on “One to One Property”:
b
M
= b
N
if, and only if M = N
•
Write each side as a power of the same
base
•
Then set exponents = and solve.

Example:
Solve 27
x+3
= 9
x-1

Example:
Solve 27
x+3
= 9
x-1
•
Solution: 3
3x+9
= 3
2x-2
Now we can set the exponents = since bases
are equal:
3x +9 = 2x -2 Sub 2x and 9 both sides
x = -11

Solve Exponential Equations Using
Natural Logarithms
1. Isolate the exponential expression on one
side
2. Take natural logarithm of both sides of
equation
3. Simplify using properties like
ln b
x
= x ln b or ln e
x
= x
4. Solve for the variable

Example
•
Solve for x: 40e
.6x
-3 = 237