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 7.5a:
Answer: The exact solution is 
and the approximate solution is
x=1.29248125036.
Solution:
The exponential term is already isolated.
Take the natural logarithm of both sides of the equation 
The exact answer is 
and the
approximate answer is 
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithm with base 5.
Check this answer in the original equation.
Check the solution by
substituting 1.29248125036 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 1.29248125036. This
means that 1.29248125036 is the real solution.
If you would like to review the answer and solution to problem 7.5b, click on problem.
If you would like to go back to the equation table of contents, click on contents.
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