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 functions under Algebra.
Problem 7.4d:
Answer:
The exact answer is 
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.
Now let's look at the second factor,
There is no real number such that 
a negative number.
The exact answer is and the approximate
answer is
Check this answer in the original equation.
Check the solution by substituting
-0.182321556794 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 -0.182321556794 for x,
then x=-0.182321556794 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: -0.182321556794. This means that -0.182321556794 is
the real solution.
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