Hi I was wondering why in a logarithm $x$ cannot be a negative number, since for the inverse graph I drew the $x$ values are only positive. In the question it asks why the first four points of the exponential function are imaginary in the logarithm.
The graphical methods are an excellent way to represent this. However, from an algebraic point of view, if you have y = $\log_2(x)$
this means that $2^y$ = x. Now think about it, 2 to the power of any number will never return a negative value.
From the graph in the other answer, you can see the following: As y -> -∞ then x -> Infinitesimal value.
As for the inverse function, as x -> -∞ then y -> Infinitesimal value.
The logarithm is the inverse function of the exponential function, $a^x, a\geq 0$ which takes on positive values. Reflect this in the line $y = x$ and see the result.