Short Answer 
The logarithmic function y = log x has a domain of (0, infinity) and an x-intercept at (1, 0). When transformed to y = log base 4 of (x-2), the function shifts 2 units right, moving the x-intercept to (3, 0).
Step 1: Understanding the Domain of Logarithmic Functions
Start with the function y = log x. The domain of this function is (0, infinity), meaning it only accepts positive values. The graph does not touch the vertical axis (y-axis) and remains to its right, reflecting that logarithms are undefined for non-positive values. This characteristic is shared by all logarithmic functions.
Step 2: Identifying the x-Intercept
Next, determine where the function y = log x crosses the x-axis. The real zero occurs at x = 1 since log 1 = 0, resulting in the point (1, 0). This point serves as the x-intercept for the graph and indicates where the output of the logarithmic function equals zero.
Step 3: Analyzing Transformed Logarithmic Functions
Finally, examine the function y = log to the base 4 of (x-2). This function has a similar shape to y = log to the base 4 of x but is translated 2 units to the right. As a result, the x-intercept shifts correspondingly to (3, 0), showing that now log to the base 4 of (3-2) = 0.