Extraneous solutions in logarithmic equations arise because logarithms are only defined for positive arguments. When solving logarithmic equations, we sometimes obtain solutions that, when plugged back into the original equation, result in taking the logarithm of a negative number or zero. These solutions are called extraneous and must be discarded. Always check your solutions!
Match each term with its definition:
| Term | Definition |
|---|---|
| 1. Logarithm | A. A solution that does not satisfy the original equation. |
| 2. Argument | B. The inverse operation to exponentiation. |
| 3. Base | C. The value inside the logarithm. |
| 4. Extraneous Solution | D. The number that is raised to a power in an exponential expression. |
| 5. Domain | E. The set of all possible input values (x-values) for which a function is defined. |
Logarithmic equations can sometimes have ___________ solutions. This happens when a solution makes the argument of the logarithm ___________ or __________. Therefore, it is crucial to ___________ your solutions by plugging them back into the original equation.
Explain, in your own words, why it's important to check for extraneous solutions when solving logarithmic equations. Give an example of a logarithmic equation that is likely to produce extraneous solutions and explain why.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀