The graph of the logarithmic function f(x) = loga(x) passes through the points and . the graph lies the y-axis.

The question is incomplete. But this explanation will help you very much.

1) Regarding the function         , its graph always passes through the points (1,0) and (a,1).

That is due to the properties of logarithm function:

a)   

b)   
 
That in turn is due to the properties of the exponential functions.

a^0 = 1 and a^1 = a

2) Regarding the y-axis.

The function will never touch the y-axis, because the logaritm of zero is not defined. So the graph lies to the righ of the y-axis (i.e. the domain of the function is x > 0)