## 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 7.7a:

Solution:

The first step is to isolate .

Subtract 14 from both sides of the equation.

Divide both sides of the equation by 2.

The next step is to isolate the variable x.

Take the natural logarithm of both sides of the equation..

Use the Quadratic Formula where a=2, b=5,

The exact answers are and the approximate answers are and - 3.618639.

Check the solution by substituting 1.118639 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: 34

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 1.118639 for x, then x=1.118639 is a solution.

Check the solution by substituting -3.618639 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: 34

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value -3.618639 for x, then x=-3.618639 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 1.118639 and -3.618639. This means that 1.118639 and -3.618639 are the real solutions.

If you would like to review the solution to problem 7.7b, click on Problem

If you would like to go back to the beginning of this section, click on Beginning

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