## 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.

Problem 7.2b:

Solution:

The first step is to isolate the exponential term. Therefore, subtract 10 from both sides of the equation

Take the natural logarithm of both sides of the equation

When solving the above problem, you could have used any logarithm. For example, let's solve it using the logarithmic with base 5.

Check this answer in the original equation.

Check the solution by substituting 4.38202663467 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 4.38202663467 for x, then x=4.38202663467 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 4.38202663467. This means that 4.38202663467 is the real solution.

If you would to review the answer and solution to problem 7.2c, click on 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 level, click on Next.

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