3.2 Solving Exponential
Equations with a Common Base
Friday!
Review: Negative Exponents
• Negative Exponent becomes POSITIVE once its
base is in its reciprocal form
24𝑝−8
16𝑝−3
3 −3
5𝑥
2𝑦 4
Solving Equations with Rational
Exponents
• To solve equations with rational exponents
(fractional exponents), RAISE both side of the
equation to the RECIPROCAL POWER of the
exponent
1
𝑥3
= −5
Exponential Equations and Functions
• Exponential Equation is an equation where the
variable is in the exponent.
3𝑥 = 3
• Exponential Function is a function where the
variable is in the exponent.
𝑓 𝑥 = 3𝑥
Solving Exponential Equations
22𝑥 = 16
• Follow the following steps to solve
exponential equation:
– Make each side of the equation as power with
SAME BASE!
– Eliminate the base, and have exponents equal to
each other
– Solve for the variable
Example
22𝑥 = 16
22𝑥 = 24
2𝑥 = 4
𝑥=2
Try: Pg. 165 # 1 abc
Square Root
• Square Root is equivalent to an
𝑥=
1
exponent
2
1
𝑥2
• Cube root is equivalent to an exponent
3
𝑥=
1
x3
1
of
3
Try..
• Pg. 165 # 1d
• Pg. 166 # 2, 3
WEEKEND
Homework
•Pg. 167 # 2-7, 9-12