A logrithmic function is defined only for positive numbers. Irrespective of base, log function has domain always numbers greater than 0.
Here given is log x to base 10.
This is not defined for x =0 or x <0
x=0 will be an asymptote for log x.
x<0 will not have any definition in log
So domain is all positive numbers >0
When x =10, log x = 1 and for x =1, log =0
Thus passes through (1,0) and (10,1)
For x<1, y log x has negative values.