It has been given that the point (3,1) is on the graph. For the point (3,1) to be on the graph, the following must hold true:
[tex] 1=log_{10}(ax) [/tex]
or [tex] ax=10^1=10 [/tex]
Thus, [tex] x=\frac{10}{a} [/tex]
Thus, in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C, that is, when a=3. That will make x=3.33 and thus, [tex] log(3\times3.33)\approx0.99957\approx1 [/tex].
Thus, out of the given options only Option C seems to be the most probable answer.
