If we are provided an equation through a logarithm the the exact same base top top both sides we might simply equate the arguments. Action 1: usage the rule of exponents to isolate a logarithmic expression (with the exact same base) top top both sides of the equation.

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step 2: set the arguments equal to each other. step 3: settle the resulting equation. action 4: check your answers.
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Be certain to inspect to see if the options that you obtainsolve the initial logarithmic equation. In this research guidewe will placed a inspect mark alongside the systems after wedetermine that it really does fix the equation. Thisprocess periodically results in extraneous solutions sowe must check our answers.Solve
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Of course, equations favor these are very special. Most of the problems that we will encounter will not have a logarithm ~ above both sides. The steps for addressing them follow. Action 1
: use the nature of the logarithm toisolatethe log on one side. step 2: apply the meaning of the logarithm and also rewrite it as an exponential equation. step 3: fix the resulting equation. action 4: examine your answers.
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If the answer to the logarithmic equation makes the argument an unfavorable then the is extraneous. This does not preclude an unfavorable answers. We have to be sure to check all of our solutions.

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Tip
: no all an adverse solutions space extraneous! Look at the previous set of problems and see that some have an unfavorable answers.The examine mark shows that we actually plugged the answers in to watch that they do without doubt solve the original. Please execute not skip this step, extraneous solutions happen often.