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.


Problem 8.2b:

tex2html_wrap_inline132


Answer:tex2html_wrap_inline155The exact answer is tex2html_wrap_inline134 or tex2html_wrap_inline136 and the approximate answer is tex2html_wrap_inline138


Solution:


Note that the domain of tex2html_wrap_inline140 is the set of real numbers such that tex2html_wrap_inline142 or when x>0, because you cannot take the log of zero or a negative number.


Isolate the logarithmic term.


eqnarray34


eqnarray38


eqnarray50


eqnarray59


eqnarray69



The exact answer is tex2html_wrap_inline146 and the approximate answer is tex2html_wrap_inline148



Check the answer tex2html_wrap_inline146 by substituting tex2html_wrap_inline152 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 1.04004191153 for x, then tex2html_wrap_inline152 is a solution.



You can also check your answer by graphing tex2html_wrap_inline162 (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 1.04004191153. This means that tex2html_wrap_inline152 is the real solutions.



If you have trouble graphing the equation tex2html_wrap_inline168 try graphing the equivalent equation tex2html_wrap_inline170






If you would like to review the solution to problem 8.2c, click on Solution


If you would like to test yourself by working some problems similar to this example, click on Problem


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Author: Nancy Marcus

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