If you would like an in-depth review of logarithms, the rules of logarithms, logarithmic functions and logarithmic equations, click on logarithmic function.
Solve for x in the following equation.
The above equation is valid only if Either x-8>0 and or x-8<0 and The domain is the set of real numbers less than -2 or greater than 8.
Convert the equation to an exponential equation with base 4.
The exact answers are and the approximate answers are 8.0131514 and -2.0131514.
These answers may or may not be the solutions. You must check them with the original equation, either by a numerical substitution or by graphing.
Check the answer by substituting 8.0131514 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 8.0131514 for x, then x=8.0131514 is a solution.
Check the answer by substituting -2.0131514 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 -2.0131514 for x, then x=-2.0131514 is a solution.
You can also check your answer by graphing
If you are graphing with your calculator you might have a problem with log base . Therefore, convert it to either base e or base 10 to graph. Most graphing calculators have these functions.
If you would like to test yourself by working some problems similar to this example, click on problem.
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