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.
Solve for x in the following equation.
Problem 7.4f:
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.
The left side of the equation is not easily factored.
Let's see if we can use the Quadratic Formula.
Note that the equation can be rewritten as 
This is a quadratic
equation in 
If it is easier for you, substitute a number, say p,
in place of 
and rewrite the equation 
as 
let's solve this equation for p.
However, the initial equation did not contain p, therefore you have to
resubstitute for p and solve for x.
There is no real number such that 
a negative number.
The exact answer is 
and the
approximate answer is These answers may or may
not be solutions to the original equations. You must check the answers in
the original equation.
Check this answer in the original equation.
Check the solution by
substituting -0.352032295516 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 -0.352032295516 for x,
then x=0-0.352032295516 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:
-0.352032295516. This means that -0.352032295516 is the real solution.
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problem.
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