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 7.7a:
Answer:
and
- 3.52526806038
Solution:
The first step is to isolate 
.
Subtract 14 from both sides of the equation.
Take the natural logarithm of both sides of the equation..
where a=2, b=5, 
and the approximate
answers are 
and - 3.618639.
Check the solution by substituting 1.118639 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.
34
Check the solution by substituting -3.618639
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.
34
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 1.118639 and -3.618639. This means that 1.118639
and -3.618639 are the real solutions.
If you would like to review the solution to problem 7.7b, click on
Problem
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