Can anyone give me a hand with this one?
loga(x) + loga(x - 2) = loga(x + 4)
You can take the log of a negative number,
but your answer is no longer "real", but complex.
A logarithm is the inverse of a power.
If $\displaystyle y=10^x$, then $\displaystyle x=\log(y)$.
$\displaystyle 10^x$ is always positive. As a result, you can only take the log of a positive number.
However, 10 raised to an imaginary number can be negative, so the log of a negative number is imaginary.
So long as you use restrict your domain to real numbers, the log of a negative number is undefined.