Note:
If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function.
Solve for x in the following equation.
Example 3:
In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.
Factor the left side of the equation
The only way that a product can equal zero is if at least one of the factors
is zero.
Now we have an equation where the exponential term is isolated. Take the
natural logarithm of both sides of the equation
Now let's look at the second factor,
Now we have a second equation where the exponential term is isolated. Take
the natural logarithm of both sides of the equation
The exact answers are and The approximate answers are
and . However these answers may or may not be the
solutions. You must check the answers with the original equation.
Check these answers in the original equation.
Check the solution by substituting
0.847297860387 in the original equation for x. If the left side of the
equation equals the right side of the equation after the substitution, you
have found the correct answer.
Check the solution by substituting -0.287682072452
in the original equation for x. If the left side of the equation equals the
right side of the equation after the substitution, you have found the
correct answer.
You can also check your answer by graphing (formed by subtracting the right side of the
original equation from the left side). Look to see where the graph crosses
the x-axis; that will be the real solution. Note that the graph crosses the
x-axis at two places: 0.847297860387 and -0.287682072452. This means
that 0.847297860387 and -0.287682072452 are the real solutions.
If you would like to test yourself by working some problems similar to this
example, click on Problem
If you would like to go to the next section, click on Next
If you would like to go back to the equation table of contents, click on
Contents.
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.