<u>Given:</u>
The given equation is
We need to determine the extraneous solution of the equation.
<u>Solving the equation:</u>
To determine the extraneous solution, we shall first solve the given equation.
Applying the log rule , we get;
Again applying the log rule, if then
Thus, we have;
Simplifying the equation, we get;
Factoring the equation, we get;
Thus, the solutions are
<u>Extraneous solutions:</u>
The extraneous solutions are the solutions that does not work in the original equation.
Now, to determine the extraneous solution, let us substitute x = 3 and x = -7 in the original equation.
Thus, we get;
Since, we know that is undefined.
Thus, we get;
Undefined = Undefined
This is false.
Thus, the solution x = 3 does not work in the original equation.
Hence, x = 3 is an extraneous solution.
Similarly, substituting x = -7, in the original equation. Thus, we get;
Simplifying, we get;
Undefined =
Undefined = 3.06
This is false.
Thus, the solution x = -7 does not work in the original solution.
Hence, x = -7 is an extraneous solution.
Therefore, the extraneous solutions are x = 3 and x = -7