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

Example 6: Solve for x in the equation



Step 1: If you graph the equation, you will note that the graph crosses the x-axis in two places, once to the left of the y-axis and once to the right of the y-axis. This means that there will be one negative real solution and one positive real solution.
Step 2: Write the equation in quadratic form and factor.


Step 3: The only way a product is zero is when one or more of the factors is equal to zero.
Step 4: If tex2html_wrap_inline60 . Take the natural log of both sides.


is the exact answer and x=0.69314718056 is an approximate answer.

Step 5: If tex2html_wrap_inline66 and tex2html_wrap_inline68 . Take the natural log of both sides.


and tex2html_wrap_inline72 is the exact answer and


is an approximate answer.

Step 6: Let check both answers with the original problem. If when the value of x is substituted in the left side of the equation, the value of the left side of the equation equals the right sides of the equation (in this case 0), you have found the correct answer. You could also check the values of x with x-intercepts on your graph. They should be the same.
Step 7: If tex2html_wrap_inline76 , then tex2html_wrap_inline78 becomes 0. If tex2html_wrap_inline80 , then tex2html_wrap_inline78 becomes 0.
Step 8: You have worked the problem correctly.

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

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Author: Nancy Marcus

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