SOLVING EXPONENTIAL EQUATIONS - Problem 4

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

Problem 4: Solve for x in the equation

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Solution:

Step 1: Graph the function

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Note that it crosses the x-axis only once between 6 and 7. This means there is just one real solution and that solution is between 6 and 7.

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

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

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Step 4: Divide both sides of the above equation by

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to get

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is the exact answer and

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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

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You can also check your answer by graphing the function

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

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

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Author: Nancy Marcus

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