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
Problem 7.1c:
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 
Check this answer in the original equation.
Check the solution by substituting -0.287682072452
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 -0.287682072452
. This means that -0.287682072452 is the real solution.
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