SOLVING EXPONENTIAL EQUATIONS Problem 5

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

Problem 5: Solve for x in the equation

displaymath57


Solution:

Step 1: Isolate the exponential term tex2html_wrap_inline59 using steps 2 through 6.
Step 2: Divide both sides of the original equation by 5000:

displaymath61

Step 3: Subtract 1 from both sides of the above equation:

displaymath63

or

displaymath65

Step 4: Multiply both sides of the above equation by tex2html_wrap_inline67 :

displaymath69

Step 5: :Divide both sides of the above equation by 0.92:

displaymath71

Step 6: Subtract 4 from both sides of the above equation:

displaymath73

Step 7: Take the natural log of both sides of the above equation:

displaymath75

Step 8: Simplify the left side of the above equation using Logarithmic Rule 3:

displaymath77

Step 9: Since Ln(e) = 1, the above equation is simplified to

displaymath77

Step 10: Divide both sides of the above equation by -0.002:

displaymath81

rounded to 528.

Check: Check the graph, it should cross in one place very close to x = 528. You can also substitute the number in the original equation and check to see if the left side of the equation then equals the right side of the equation.

If you want to work 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