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 7.2a:
Answer: 
The exact answer is 
and the approximate answer
is 
Solution:
The first step is to isolate the exponential term. Therefore, add 8 to
both sides of the equation 
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 5.
Check this answer in the original equation.
Check the solution by substituting 2.56494935746 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 2.56494935746. This
means that 2.56494935746 is the real solution.
If you would to review the answer and solution to problem 7.2b, click
on Solution.
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