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 3:
The first step is to isolate the expression 
Add 8 to both sides of the equation.
Divide both sides of the equation by 14.
Take the natural logarithm of both sides of the equation 
The exact answer is 
and the approximate answer is 
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithm with base 9.
Check this answer 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.
is a solution.
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 1.828866. This means that 1.828866 is the real solution.
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
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