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

Solution:

Step 1: Isolate the exponential term by subtracting 10 from both sides of the above equation:

Step 2: Since the base is 6, let's take the take

of both sides:

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

Step 4: Simplify the left side of the above equation: Since

, the above equation can be written

Step 5: Add 8 to both sides:

Step 6: Divide both sides by 3:

is the exact answer and

displaymath70

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

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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