EXPONENTIAL EQUATIONS
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 the real number x in the following equation.
Problem 7.1b:
Answer:
The exact answer is 
and the approximate answer
is 
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 logarithmic with base 112.
Check this answer in the original equation.
Check the solution by substituting 4.499980967033 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 4.499980967033. This
means that 4.499980967033 is the real solution.
If you would like to review the answer and the solution to problem 7.1c, click on Solution.
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