SOLVING EXPONENTIAL EQUATIONS - Example

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

Example 9: Solve for x in the equation

Solution:

Step 1: If you graph

you will note that the graph crosses the x-axis at the origin. This means there is only one solution and that solution is 0.

Step 2: Isolate the exponential term

using steps 2 through 7.

Step 3: Divide both sides of the original equation by 3: The expression

can now be written

Step 4: Take the cube root of both sides:

Step 5: Add 5 to both sides:

Step 6: Divide both sides by 7:

Step 7: By now you should recognize that the value of x has to be 0. If you do not, take the natural log of both sides:

which can be written .

Check: Let's check the answer with the original problem. When we substitute the 0 for the value of x in the left side of the equation, we get

We have proved our answer.

If you would like to work a problem, click on problem.