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

Example 9: Solve for x in the equation



Step 1: If you graph


you will note that the graph crosses the x-axis at the origin. This means there is only one solution and that solution is 0.

Step 2: Isolate the exponential term tex2html_wrap_inline53 using steps 2 through 7.
Step 3: Divide both sides of the original equation by 3: The expression


can now be written


Step 4: Take the cube root of both sides: tex2html_wrap_inline59
Step 5: Add 5 to both sides: tex2html_wrap_inline61
Step 6: Divide both sides by 7: tex2html_wrap_inline63
Step 7: By now you should recognize that the value of x has to be 0. If you do not, take the natural log of both sides:


which can be written tex2html_wrap_inline67 .

Check: Let's check the answer with the original problem. When we substitute the 0 for the value of x in the left side of the equation, we get


We have proved our answer.

If you would like to work a problem, click on problem.

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Author: Nancy Marcus

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