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Answer: The exact answer are and the approximate answer is
In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.
Factor the left side of the equation
The only way that a product can equal zero is if at least one of the factors is zero.
There is no real value of x such that can be a negative number.
Now let's look at the second factor,
Now we have a second equation where the exponential term is isolated. Take the natural logarithm of both sides of the equation
The exact answer is and the approximate answer is
Check this answer in the original equation.
Check the solution by substituting 1.09861228867 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 1.09861228867 for x,
then x=1.09861228867 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 one place: 1.09861228867. This means that 1.09861228867 is the real solution.
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