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

Solution:

Step 1: Isolate the exponential term

using steps 2 through 4.

Step 2: Multiply both sides of the above equation by

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

Step 4: Add 2 to both sides of the above equation:

Step 5: Since the base is 7, let's take

of both sides:

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

Step 7: We know that

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

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

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

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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