3.4
Exponential and Logarithmic Equations
exponential equation
– equation containing a variable in an exponent.
Ex:
Solving Exponential Equations by Expressing Each Side as a Power of the Same Base
If
N
M
b
b
=
, then M = N.
1.)
Rewrite the equation in the form
N
M
b
b
=
2.)
Set M = N
3.)
Solve for the variable
EX 1:
Solve
a)
b)
c)
Using
to solve Exponential Equations
1.) Isolate the exponential expression
2.) Take the
of both sides unless base is 10 then take
log
of both sides.
3.) Simplify using one of the following properties:
x
e
or
b
x
b
x
x
=
=
ln
ln
ln
or
x
x
=
10
log
4.) Solve for the variable.
EX 2:
Solve
134
5
=
x
EX 3:
Solve
58
5
7
2
=

x
e
EX 4:
Solve
1
1
2
7
3
+

=
x
x
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View Full DocumentEX 5:
Solve
0
7
8
2
=
+

x
x
e
e
Logarithmic Equations
 A logarithmic equation is an equation containing a variable in a logarithmic expression.
Ex:
Use the Definition of Logarithm to Solve Logarithmic Equations
1.)
Express the equation in the form
c
M
b
=
log
2.)
Use the definition of logarithm to rewrite in exponential form:
M
b
c
=
3.)
Solve for the variable.
4.)
Check proposed solutions in the original equation.
Include in the solution set only values for which
M>0.
EX 6:
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 Fall '08
 Mcbride,V
 Exponential Function, Logarithmic Equations, Equations, ex, Natural logarithm, Logarithm

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