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.
Problem 7.4c:
Answer:
The exact answer
are 
and the approximate answer is 
Solution:
In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.
Factor the left side of the equation 
The only way that a product can equal zero is if at least one of the factors
is zero.
There is no real value of x such that 
can be a negative
number.
Now let's look at the second factor,
Now we have a second equation where the exponential term is isolated. Take
the natural logarithm of both sides of the equation 
The exact answer is and the approximate answer is
Check this answer in the original equation.
Check the solution by substituting 1.09861228867
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.
Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value 1.09861228867 for x,
then x=1.09861228867 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 one place:
1.09861228867. This means that 1.09861228867 is the real solution.
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