SOLVING EXPONENTIAL EQUATIONS - Example

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

Example 5: Solve for x in the equation

displaymath62


Solution:

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 :

displaymath68

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

displaymath70

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:

displaymath76

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

displaymath78

Step 7: We know that

displaymath80

(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:

displaymath86

is the exact answer.

displaymath88

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

displaymath90

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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