Graphing a Logarithm - Mr. C's Method

Yesterday I was thinking of a quick way to graph a logarithmic function involving both horizontal and vertical shifts. After much pondering, I figured something out and wanted to share it with you; I'm calling it Mr. C's Method (for now)! Note that there is some building up of background information prior to the "trick", though. So, if you're itching to jump right into it, go ahead and skip to 6:26.
Side note: The gorgeous Corgi in the thumbnail is Pretzel. She is the "middle child" of the 3 Corgis that we have. I don't think she had any interest in being featured in a math video, though, LOL!