SOLVING EXPONENTIAL EQUATIONS - Example

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

Example 1: Solve for x in the equation

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Solution:

Step 1: Isolate the exponential term by subtracting 10 from both sides of the above equation: tex2html_wrap_inline54 .
Step 2: Since the base is 6, let's take the take tex2html_wrap_inline56 of both sides:

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Step 3: Simplify the above equation using Logarithmic Rule 3:

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Step 4: Simplify the left side of the above equation: Since tex2html_wrap_inline62 , the above equation can be written

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Step 5: Add 8 to both sides:

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Step 6: Divide both sides by 3:

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is the exact answer and

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rounded to 3.328 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

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Close enough to 45. 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 45 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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