Question

Let g(x)=log4(x^2-4x-21). Find the domain of g(x).

Answer 1

\[g(x)=\frac{\ln(x^2-4x-21)}{\ln(4)} \text{ domain is } x^2-4x-21>0\]

Answer 2

make sure that the mess inside the log is positive, because you cannot take the log of a negative number. in other words solve
\[x^2-4x-21>0\] for x

Answer 3

you do this via
\[(x-7)(x+3)>0\] and this is a parabola that opens up, so it will be negative between the zeros and positive outside of them. your answer therefore will be
\[(-\infty,-3)\cup (7,\infty)\]

Answer 4

THANKS!!!