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Solving Exponential and Logarithmic Equations

C. Solve

Of course, equations like these are very special. Most of the problems that we will encounter will not have a logarithm on both sides, as with the next set.
If the answer to our logarithmic equation makes the argument of it negative then it is extraneous. This does not preclude negative answers. We must be sure to check all of our solutions.

   
Step 1: Use the rules for logarithms to isolate a log..
Step 2: Apply the definition of the logarithm and change it to an exponential equation
  Step 4: We must check to see if the solutions work .

Step 3: Solve for the variable .

Tip: Not all negative solutions are extraneous! Look at the fol lowing problems and we can see that some have negative answers.

D. Solve

The check mark indicates that we actually plugged the answers in to see that they do indeed solve the original . Please do not skip this step , extraneous solutions occur often.

Be sure to check all solutions to logarithmic equations because some might be extraneous!

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