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.
The exponential term is already isolated.
Take the natural logarithm of both sides of the equation
Check the solution
If you would like to review the answer and solution to problem 7.5d, click
on problem.
If you would like to go back to the equation table of contents, click on
contents.
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Problem 7.5c: 
Answer: The exact solution is 
and the approximate solution is x = 8.54956933001.
Solution:
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 37.
Check this answer in the original equation.
by substituting 8.54956933001 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 8.54956933001 for x,
then x=8.54956933001 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 8.54956933001. This
means that 8.54956933001 is the real solution.
