## SOLVING EXPONENTIAL EQUATIONS

Note:

• To solve an exponential equation, isolate the exponential term, take the logarithm of both sides and solve.

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.

Example 1:

The exponential term is already isolated.

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 5.

Check this answer in the original equation.

Check the solution by substituting 4.27333311902 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.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 4.27666611902 for x, then x=4.27666611902 is a solution.

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 4.27666611902. This means that 4.27666611902 is the real solution.

If you would like to work another example, click on Example

If you would like to test yourself by working some problems similar to this example, click on Problem.

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.

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Nancy Marcus