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 the real number x in the following equation.
Problem 7.6 e:
The approximate answer is
Your first objective is to isolate the term.
Add to both sides of the equation .
Multiply both sides of the equation by 3.
Your second objective 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
Check this answer 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.
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 This means that 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.
S.O.S. MATHematics home page
Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.