SOLVING EXPONENTIAL EQUATIONS
SOLVING EXPONENTIAL EQUATIONS 
Note:
If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function.
Solve for x in the following equation.
Problem 7.6b:
Answer:
Exact answer:
Approximate
answer:
Solution:
The first step is to isolate 
Add 10 to both sides of the equation.
Divide both sides of the equation by 6.
The next is to isolate the variable x.
Take the natural logarithm of both sides of the equation 
The exact answer is 
and the approximate answer is 
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithm with base 12.
Check this answer in the original equation.
Check the solution by substituting 6.72105705435 in the original
equation for x. If the left side of the equation equals the right side of
the equation after the substitution, you have found the correct
answer.
You can also check your answer by graphing 
(formed by subtracting the right side of the
original equation from the left side). Look to see where the graph crosses
the x-axis; that will be the real solution. Note that the graph crosses the
x-axis at 6.72105705435. This means that 6.72105705435 is the real
solution.
If you would like to go back to the beginning of this section, click on
Beginning
If you would like to go to the next section, click on click on
Next
If you would like to go back to the equation table of contents, click on
Contents
This site was built to accommodate the needs of students. The topics and
problems are what students ask for. We ask students to help in the editing
so that future viewers will access a cleaner site. If you feel that some of
the material in this section is ambiguous or needs more clarification,
please let us know by e-mail.
