If us are given an equation through a logarithm of the very same base ~ above both political parties we may simply equate the arguments. Action 1: usage the rule of index number to isolate a logarithmic expression (with the exact same base) ~ above both political parties of the equation.

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action 2: collection the arguments equal to every other. action 3: solve the result equation. action 4: check your answers.
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Be certain to examine to check out if the services that you obtainsolve the initial logarithmic equation. In this research guidewe will placed a check mark beside the solution after wedetermine that it yes, really does resolve the equation. Thisprocess occasionally results in extraneous options sowe must check our answers.Solve
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Of course, equations choose these are an extremely special. Many of the problems that we will encounter will certainly not have a logarithm top top both sides. The procedures for addressing them follow. Step 1
: usage the nature of the logarithm toisolatethe log on one side. action 2: apply the an interpretation of the logarithm and rewrite it as an exponential equation. step 3: settle the resulting equation. action 4: inspect your answers.
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If the answer to the logarithmic equation makes the argument negative then the is extraneous. This does not preclude an adverse answers. We have to be sure to check every one of our solutions.

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Tip
: not all an unfavorable solutions room extraneous! Look in ~ the previous collection of problems and also see that some have an adverse answers.The check mark shows that we in reality plugged the answers in to see that they do indeed solve the original. Please perform not skip this step, extraneous solutions take place often.