Download Solving Exponential Equations Solving Exponential Equations

11/11/2014
5.3: Exponential and Logarithmic
Equations
Solving Exponential Equations
Change of Base
Solving Logarithmic Equations
Solving Exponential Equations
= ( )
Using logarithmic
form:
Rewrite the equation
with the term
containing the
exponent by itself on
one side.
Divide both sides by
the coefficient of the
term containing the
exponent.
Change the new
equation to
logarithmic form.
Solve for the
variable.
The term containing the
exponent is already by
itself.
Divide both sides by
150 (the coefficient)
20 = 10
4 = 20
=
20
≈ 0.32526
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Solving Exponential Equations
= Using logarithmic
properties:
Rewrite the equation
with a base raised to
a power on one side.
Take the logarithm,
base e (ln) or 10, of
both sides of the
equation.
Use a logarithmic
property to remove
the variable from the
exponent.
Solve for the variable.
The equation already
has a base raised to a
power.
Take the log base 10
4096 = 8!"
Power Property of Logarithms
4096 = 2#8
4096
==
28
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11/11/2014
Change of Base
Used to rewrite logarithms so that
the base is 10 or e
For base 10 and base e
$ # =
%&' "
%&' $
$ # =
%( "
%( $
Solving Logarithmic Equations
Graphically
Graph the left and right sides of the
equation separately
Find the point of intersection
Algebraically
Convert to exponential form
Solve
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