Question 1032364
(a) {{{log(2,0)}}} is undefined because there is NO real number x such that {{{2^x = 0}}}.  

(b)  {{{ log(2, x)}}} is negative when x is between 0 and 1 because, if you will notice the graph of {{{y=2^x}}}, for {{{0 < y=2^x <1}}}, the corresponding set of pullback x-values is exactly the interval ({{{-infinity}}}, 0).
{{{graph( 300, 200, -5, 5, -5, 5, 2^x)}}}

(c)  This is easy, because {{{2^8 =256 < 500 < 2^9=512}}}.

(d)  An x can be found so that {{{log(2,x)}}} is greater than 1,000,000.  Indeed, {{{2^20 }}} =  1,048,576 > 1,000,000.

You have to remember that logarithm is just a fancy way of writing an exponent satisfying a base condition.