SOLVING EXPONENTIAL EQUATIONS
SOLVING EXPONENTIAL EQUATIONS 
Note:
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Solve for the real number x in the following equation.
Problem 7.7 c:
The exact answer is 
.
The approximate answers are 
and
- 6.046449 .
Solution:
Your first objective is to isolate the term 
.
Add 
to both sides of the equation .
.
Take the natural logarithm of both sides of the equation .
where a=1, b=5, 
.
and the approximate
answers are and - 6.046449 .
Check this answer in the original equation.
Check the solution by substituting 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.
for x, then x=1.1092880431 is a solution.
Check the solution by substituting 
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.
for
x, then x=-6.046449 is a solution.
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 
This means that and -6.046449
are the real solutions.
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