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.
Solve for x in the following equation.
Problem 7.3c:
Answer:
The exact answers are 
The approximate answers are 
and 1.89818568407.
There are many forms of the exact answer; however, all forms will have the same approximate answer.
Solution:
Isolate the exponential term in the equation 
.
Divide both sides of the equation by 2
Take the natural logarithm of both sides of the equation 
Solve for x using the quadratic formula 
where 
The exact answers are 
and the approximate answers are and
1.89818568407.
Check these answers in the original equation.
Check the solution 
by substituting 1.89818568407 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.
Check the solution 
by substituting 0.60181431593 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 0.60181431593 and 1.89818568407. This means that
0.60181431593 and 1.89818568407 are the real solutions.
If you would to review the answer and solution to problem 7.3d, click
on Solution.
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