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.
under Algebra.
Solve for x in the following equation.
Example 4:
Isolate the exponential term.
Note that the base is e, not 
Multiply both sides of
the equation by 
Take the natural logarithm of both sides of the equation 
The exact answer is 
and
the approximate answer is 
Your exact answer may differ dependent how what logarithm you used to solve
the problem. However, all forms of the correct answer will simplify to the
same approximate answer.
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithmic with base 14. Take the 
of both sides of the equation
The exact answer is and
the approximate answer is
Check these answers in the original equation.
Check the solution by
substituting 1.11693268486 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 1.11693268486.. This means that 1.11693268486 is the real
solution.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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