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.
Problem 7.3b:
Answer:
The exact answer is 
The approximate answer is 
.
There are many forms of the exact answer; however, all forms will have the same approximate answer.
Solution:
Isolate the exponential term.
Divide both sides of the equation by 23
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 7.
The exact answer is 
and
the approximate answer is 0.420217818828.
Although this exact answers
looks different from the above exact answer, they are equivalent: both have
the same approximate answer.
Check this answer in the original equation.
Check the solution by substituting 0.420217818828 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 0.420217818828. This means that 0.420217818828 is the real
solution.
If you would to review the answer and solution to problem 7.3c, click
on Solution.
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