## 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 2: The first step is to isolate the expression Subtract 14 from both sides of the equation.  Divide both sides of the equation by 12.  Take the natural logarithm of both sides of the equation      Use the Quadratic Formula where a=1, b=-9, .       The exact answers are and the approximate answers are and Check these answers in the original equation.

Check the solution by substituting 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: 38

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 8.05483513081 for x, then x=8.05483513081 is a solution.

Check the solution by substituting 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: 38

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 0.94516486919 for x, then x=0.94516486919 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 8.05483513081 and 0.94516486919. This means that 8.05483513081 and 0.94516486919 are the real solutions.

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] S.O.S. MATHematics home page

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