SOLVING EXPONENTIAL EQUATIONS - Example

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

Example 7: Solve for x in the equation

Solution:

Step 1: Isolate the exponential term tex2html_wrap_inline62

by dividing both sides by 500:

Step 2: Take the Ln of both sides of the above equation:

Step 3: Use Logarithmic Rule 3 to simplify the left side of the above equation:

Step 4: Divide both sides of the above equation by tex2html_wrap_inline70

displaymath72

is the exact answer and is the approximate answer.

Check: Let's check the approximate answer with the original problem. When we substitute the above value of x in the left side of the equation, we get

You can also check your answer by graphing the function

and note where the graph crosses the x-axis. If you have worked the problem correctly, it should be the same value of x.

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

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Author: Nancy Marcus