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 first objective is to isolate the expression 
.
Subtract 5 from both sides of the equation.
Take the natural logarithm of both sides of the equation
.
Use the Quadratic Formula 
where a=1, b=-6, 
.
and
The exact answers are and the approximate answers are 
and 
Check these answers in the original equation.
Check the solution by substituting 5.88954754282 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 0.110452457185 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 5.88954754282 and 0.110452457185. This means that
5.88954754282 and 0.110452457185 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 back to the equation table of contents, click on contents.
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