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:
Isolate the exponential term.
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 logarithmic with base 6.
Check this answer in the original equation.
Check the solution 
by substituting -0.980829253012
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
-0.980829253012. This means that -0.980829253012 is the real solution.
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
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