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.
Example 2:
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.
This is impossible. Therefore, If you did not make this
observation, you would have caught it when you tried to take the natural
logarithm of both sides since you cannot take the logarithm of 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
x=1.09861228867.
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.
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.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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