SOLVING EXPONENTIAL EQUATIONS - Example

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

Example 8: Solve for x in the equation

Solution:

Step 1: Isolate the exponential term

using steps 2 through 6.

Step 2: Divide both sides of the above equation by 2000:

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

Step 4: Multiply both sides of the above equation by

Step 5: Divide both sides of the above equation by 0.95:

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

Step 7: There is no way that the positive number e raised to a power will yield a negative number. There is no solution.

You could also graph the function

and note that the graph does not cross the x-axis. This means there is no real solution.

If you would like to review another example, click on Example.