SOLVING EXPONENTIAL EQUATIONS - Problem 3

To solve an exponential equation, take the log of both sides, and solve for the variable.

Problem 3: Solve for x in the equation

displaymath50


Solution:

Step 1: If you graph the left side of the above equation, you will note that the graph crosses the x-axis in two places, once to the left of the y-axis and once to the right of the y-axis. This means that there will be one negative real solution and one positive real solution.
Step 2: Write the equation in quadratic form and factor:

displaymath52

Step 3: The only way a product of two factors is zero is when one or both of the factors is equal to zero.
Step 4: If tex2html_wrap_inline54 and tex2html_wrap_inline56 . Take the natural log of both sides.

displaymath58

is the exact answer and x=0.916290731874 is an approximate answer.

Step 5: If tex2html_wrap_inline62 and

displaymath64

Take the natural log of both sides. tex2html_wrap_inline66 and

displaymath68

is the exact answer and

displaymath70

is an approximate answer.

Check: Let check both answers with the original problem. If when the value of x is substituted in the left side of the equation, the value of the left side of the equation equals the right side of the equation (in this case 0), you have found the correct answer. You could also check the values of x with the x-intercepts on your graph. They should be the same.

They do and you have worked the problem correctly.

If you would like to review another problem, click on Next Problem.

[Previous Problem] [Next Problem] [Menu Back to Solving EE]

[Algebra] [Trigonometry] [Complex Variables]

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

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour