1.  x-intercept is the point where y = ln(x) = 0.

    It is the point where the plot y = ln(x) intersect x-axis.

    From  ln(x) = 0   you have  x = 1.

    Hence, the point x = 1 is x-intercept.



2.  There is NO y-intercept

    y-intercept is the point on the plot at x = 0.

    But x = 0 does not belong to the domain of the ln function.



3.  The domain of the the function y = ln(x) is the set of all positive real numbers.

    You can take and calculate ln(x) for any positive real number x.

    You can not take logarithm of 0 (zero) or negative number.



4.  The range of the function y = ln(x) is the set of all real numbers.

    To get it, simply look into the plot of this function (below).





          Plot y = ln(x)