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 1:
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.
Now we have an equation where the exponential term is isolated. Take the
natural logarithm of both sides of the equation
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 answers are x=0 and
Check these answers in the original equation.
Check the solution x=0 by substituting 0 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.
Check the solution by substituting 0.69314718056 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 two places: 0 and
0.69314718056. This means that 0 and 0.69314718056 are the real
solutions.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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Contents.
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