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_inline58


Note that the domain of tex2html_wrap_inline60 is the set of real numbers greater than zero because you cannot take the log of zero or a negative number.

eqnarray20


The exact value is tex2html_wrap_inline62 and the approximate value tex2html_wrap_inline64




Check the solution tex2html_wrap_inline62 by substituting 20.085537 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 20.085537 for x, then x=20.085537 is a solution.




You can also check your answer by graphing tex2html_wrap_inline78 (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 20.085537. This means that 20.085537 is the real solution.



If you would like to work another example, click on Example.


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


If you would like to go back to the equation table of contents, click on Contents.


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Author: Nancy Marcus

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