SOLVING EXPONENTIAL EQUATIONS
SOLVING EXPONENTIAL EQUATIONS 
Note:
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Solve for x in the following equation.
Problem 7.6b:
Answer:
Exact answer:
Approximate
answer:
Solution:
The first step is to isolate 
Add 10 to both sides of the equation.
Divide both sides of the equation by 6.
The next is to isolate the variable x.
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 logarithm with base 12.
Check this answer in the original equation.
Check the solution by substituting 6.72105705435 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 6.72105705435. This means that 6.72105705435 is the real
solution.
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