When does an extraneous solution occur? How can an extraneous solution be recognized? Check ALL that apply. It can be recognized by plugging it back into the original equation; if it makes the argument of the logarithmic function a positive real number, it is an extraneous solution It can be recognized by plugging it back into the original equation; if it makes the argument of the logarithmic function zero or a negative real number, it is an extraneous solution It is a solution that occurs when a logarithmic equation is solved, and one or more of the solutions turn out to be a valid input for the original equation It is a solution that occurs when a logarithmic equation is solved, and one or more of the solutions turn out to be an invalid input for the original equation.

Extraneous solutions often pop up when you manipulate equations, especially logarithmic ones. When solving, it's easy to inadvertently introduce solutions that don't really "fit" the original problem. For example, if you take the log of a negative number during your calculations, you might derive a solution that seems legit but doesn't actually work back in the original equation. Always double-check your findings! To spot these pesky extraneous solutions, always bring the number back to the original equation. If it gives you a negative or zero input for a logarithm, then bingo! You’ve found an extraneous solution. Conversely, if the solution leads to a positive argument for the log function, it might just be valid. So remember, verification is key to ensuring your solutions are truly the right ones!