Graphing log graphs are no where near that complicated. Is this how you have to do it?

You can graph any log graph by shifting the general form of the log graph. See below:

All graphs of the form looks like that. I do not care what the base is. They all pass through (1,0), shape like a square root graph and are asymptotic to the y-axis. To get the graph , you take the graph you see below, shift it 5 units to the right (so the asymptote shifts as well, 5 units, and ends up at the line x = 5). Then shift that graph 3 units up (because of the + 3). Now you would simply solve for the x- and y-intercepts. There are no y-intercepts as you can probably tell. to find the x-intercept, set y = 0 and solve for x. then you will know where you graph touches the x-axis