©
:
Pre

Calculus

Chapter 6A
Chapter 6A

Exponential and Logarithmic Equations
Exponential Equations
In previous chapters we learned about the exponential and logarithmic functions, studied some of their
properties, and learned some of their applications. In this chapter we show how to solve some simple
equations which contain the unknown either as an exponent (exponential equation) or as the argument
of a logarithmic function.
As a general rule of thumb
,
to solve an exponential equation proceed as
follows
:
1
.
Isolate the expression containing the exponent on one side of the equation.
2
.
Take the logarithm of both sides to ”bring down the exponent”.
3
.
Solve for the variable.
Example 1
:
Solve 3
x
25
Solution:
3
x
25
take the natural log of both sides
x
ln3
ln25
solve for
x
x
ln25
ln3
≈
2. 929947
Example 2
:
Solve 4
3
x
1
8
Solution:
4
3
x
1
8
isolate
x
3
x
1
4
take the natural log of both sides
x
1
ln3
ln4
solve for
x
x
ln4
ln3
−
1
≈
. 2618595
Example 3
:
Solve the equation
10
1
e
−
x
2
Solution We need to “isolate” the terms involving
x
on one side of the equation. We can do this by
cross multilpying and then solving for
e
−
x
:
1
e
−
x
5
e
−
x
4
−
x
ln4
x
−
ln4
≈ −
1. 386294
©
:
Pre

Calculus
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