SOLVING EXPONENTIAL EQUATIONS
SOLVING EXPONENTIAL EQUATIONS
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 2:
The first step is to isolate the expression 
Subtract 14 from both sides of the equation.
Divide both sides of the equation by 12.
Take the natural logarithm of both sides of the equation 
Use the Quadratic Formula 
where a=1, b=-9, 
.
The exact answers are and the approximate answers are 
and 
Check these answers in the original equation.
Check the solution by substituting 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.
38
Check the solution 
by substituting 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.
38
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 8.05483513081 and 0.94516486919. This means that
8.05483513081 and 0.94516486919 are the real solutions.
If you would like to work another example, click on example.
If you would like to test yourself by working some problems similar to this example, click on problem.
If you would like to go back to the equation table of contents, click on contents.
