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 2:

tex2html_wrap_inline99


Note that the domain of tex2html_wrap_inline101 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.



eqnarray21


eqnarray23



Convert the logarithmic equation to an exponential equation.


eqnarray32


eqnarray38


eqnarray45



The exact answer is tex2html_wrap_inline103 and the approximate answer tex2html_wrap_inline105



Check the answer tex2html_wrap_inline107 by substituting 0.825505404066 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 0.825505404066 for x, then x=0.825505404066 is a solution.


You can also check your answer by graphing tex2html_wrap_inline119 (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 0.825505404066 . This means that 0.825505404066 is the real solution.








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