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 8.2c:


Answer:tex2html_wrap_inline155The exact answer is tex2html_wrap_inline158 and the approximate answer is tex2html_wrap_inline160


Note that the domain of tex2html_wrap_inline162 is the set of real numbers such that 5 - 2x > 0, or when tex2html_wrap_inline166 because you cannot take the log of zero or a negative number. If any of your answers are greater than or equal to tex2html_wrap_inline168 , you must discard them as extraneous solutions.

Let's start the process to find the solution to the equation.

Isolate the logarithmic term.



Convert the logarithmic equation to an exponential equation with base e.


Solve for x by isolating x.



The exact answer is tex2html_wrap_inline158 and the approximate answer is tex2html_wrap_inline172

Check the answer tex2html_wrap_inline174 by substituting tex2html_wrap_inline176 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 tex2html_wrap_inline182 for x, then tex2html_wrap_inline176 is a solution.

You can also check your answer by graphing tex2html_wrap_inline186 (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 tex2html_wrap_inline182 . This means that tex2html_wrap_inline176 is the real solution.

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

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

If you would like to go to the next section, click on Next

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