SOLVING LOGARITHMIC EQUATIONS

Note:

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.


Example 3:

tex2html_wrap_inline92


Note that the domain of tex2html_wrap_inline94 is the set of real numbers such that x-8>0 or x>8 because you cannot take the log of zero or a negative number


Isolate the logarithmic term.


eqnarray22


eqnarray24


eqnarray30



Convert the logarithmic equation to an exponential equation..


eqnarray35


eqnarray41



The exact answer is tex2html_wrap_inline100 and the approximate answer tex2html_wrap_inline102



Check the answer tex2html_wrap_inline104 by substituting tex2html_wrap_inline106 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 10.3009758909 for x, then tex2html_wrap_inline106 is a solution.


You can also check your answer by graphing tex2html_wrap_inline116 (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 10.3009758909. This means that tex2html_wrap_inline106 is the real solution.








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