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

Example 5: Solve for x in the equation



Step 1: Isolate the exponential term tex2html_wrap_inline64 using steps 2 through 4.
Step 2: Multiply both sides of the above equation by tex2html_wrap_inline66 :


Step 3: Divide both sides of the above equation by 20:


Step 4: Add 2 to both sides of the above equation: tex2html_wrap_inline72
Step 5: Since the base is 7, let's take tex2html_wrap_inline74 of both sides:


Step 6: Logarithmic Rule 3 allows to simplify the left side:


Step 7: We know that


(that's why we choose tex2html_wrap_inline74 ). Therefore, the left side of the equation can be simplified to tex2html_wrap_inline84 .

Step 8: Divide both sides of the above equation by 3:


is the exact answer.


rounded to 0.6768 is an approximate answer because we rounded.

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


Close enough to 20. Remember it will not check directly because we rounded the answer. If you choose to round to only 2 or 3 decimals, the difference between the check answer and 20 would be greater.

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

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Author: Nancy Marcus

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