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

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Solution:

Step 1: Isolate the exponential term tex2html_wrap_inline57 using steps 2 through 6.
Step 2: Divide both sides of the above equation by 2000:

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

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or

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Step 4: Multiply both sides of the above equation by tex2html_wrap_inline65 :

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

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

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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

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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.

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Author: Nancy Marcus

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