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 8.2d:


Answer: tex2html_wrap_inline155The exact answer is tex2html_wrap_inline120 and the approximate answer is tex2html_wrap_inline122


Note that the domain of tex2html_wrap_inline124 is the set of real numbers such that tex2html_wrap_inline126 or when tex2html_wrap_inline128 because you cannot take the log of zero or a negative number.

Isolate the logarithmic term.




Convert the logarithmic equation to an exponential equation.



The exact answers are tex2html_wrap_inline130 and the approximate answer is tex2html_wrap_inline132

Check the answer tex2html_wrap_inline130 by substituting tex2html_wrap_inline136 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 1.06045347096 for x, then tex2html_wrap_inline136 is a solution.

You can also check your answer by graphing tex2html_wrap_inline146 (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 1.06045347096. This means that tex2html_wrap_inline136 is the real solution.

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