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 1: 
The exponential term is already isolated.
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 5.
Check this answer in the original equation.
Check the solution 
by substituting 4.27333311902 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.
Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value 4.27666611902 for x,
then x=4.27666611902 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 4.27666611902. This
means that 4.27666611902 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 Contents.
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