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 1:

tex2html_wrap_inline85

Note that the domain of tex2html_wrap_inline87 is the set of real numbers greater than zero because you cannot take the log of zero or a negative number


Isolate the logarithmic term.


eqnarray22



Convert the logarithmic equation to an exponential equation.


eqnarray29



The exact answer is tex2html_wrap_inline89 and the approximate value tex2html_wrap_inline91



Check the answer tex2html_wrap_inline89 by substituting 2.46301869964 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 2.46301869964 for x, then x=2.463018699647 is a solution.


You can also check your answer by graphing tex2html_wrap_inline105 (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 2.46301869964 . This means that 2.46301869964 is the real solution.








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Author: Nancy Marcus

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