Solving Equations with One Log Term
In the next three examples, the variable x represents the base of the
logarithm. Remember, the base of a logarithm must be positive but not 1.
Example 1
Solve: logx 100 = 2.
| Solution
Rewrite in exponential form.
Take the square root of each side.
Simplify. |
logx100 = x2
=
x =
x = |
2 100
± 10 |
Since x is the base, it must be positive. Therefore, -10 is not a solution.
The solution is x = +10.
So, log10100 = 2. The solution checks since 102 = 100. You may also
check the solution on a calculator.
Example 2
Solve:
| Solution |
logx 8 |
 |
| Rewrite in exponential form.
Rewrite using a radical.
Square both sides. |
x1/2
x |
= 8 = 8
= 64 |
So,
Note:
The solution of
is x = 64.
Here is a check.
Example 3
Solve:
| Solution |
|
|
Rewrite in exponential form.
Rewrite x-2 as
 . |
 |
| Cross multiply.
Take the square root of each side.
Simplify. |
x2 = 16 x = ±
x = ± 4 |
Since x is the base, it must be positive. Therefore, -4 is not a solution.
The solution is x = + 4.
So,
We leave the check to you.
