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 7.6f: 
Answer:
Exact answer:
Approximate answer: 
Solution:
The first step is to isolate 
Add 
to both sides of the equation.
Multiply both sides of the equation by 
.
The next step is to isolate the variable x.
Take the natural logarithm of both sides of the equation..
The exact answer is 
and the approximate
answer is 
Check the solution by substituting 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 the function 
(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 1.9039. This means
that 1.9039 is the real solution.
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