Note:
If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function. under Algebra.
Solve for x in the following equation.
Example 3:
Isolate the exponential term.
Divide both sides of the equation by 8
Take the natural logarithm of both sides of the equation
The exact answers are and
the approximate answers are -0.664200382745 and -6.33579961726.
Your exact answer may differ dependent how what logarithm you used to solve
the problem. However, all forms of the correct answer will simplify to the
same approximate answer.
When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithmic with base 29.
The exact answers are and
the approximate answers are -0.664200382745 and -6.33579961726.
Check these answers in the original equation.
Check the solution by
substituting -0.664200382745 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 -6.33579961726 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 -6.33579961726 and -0.664200382745.. This means that
-6.33579961726 and -0.664200382745 are the real solutions.
If you would like to test yourself by working some problems similar to this
example, click on Problem
If you would like to go back to the equation table of contents, click on
Contents.
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