Option c: x=6 is a true solution and x=-6 is an extraneous solution.
Explanation:
The equation is
Dividing both sides of the equation by 2, we get,
Simplifying,
Since, we know by the logarithmic definition, if , then
Using this definition, we have,
Hence,
Now, let us verify if is the solution.
Substitute in the equation to see whether both sides of the equation are true.
We have,
Using the log rule,
We have,
Hence, both sides of the equation are equal.
Thus, is the true solution.