I am currently writing an essay and am wondering if there/ what is the official name of the $\log(-x)$ graph. The searches that I have found seem to only give me that is inverse logarithmic, however, this seems to not be correct. Hopefully, someone could help me figure out what the official name of this graph is.
Thanks.
As Shubham Johri commented, $\log(-x)$ is just “the reflection of $\log x$ across the $y$ axis.” It doesn't have an special name; we translate, scalate and reflect functions in mathematics all the time. However, $\log(-x)$ is not an inverse logarithmic, since $\log(\log(-x)) \neq x$; the inverse of a logarithmic function is an exponential function (of the same base), actually.
As for the shifted graph you attached, it seems to be $x=7−9^{y−2}$ (or $y=2+\log_9(7−x)$), but I would need to see if the point $(−2,3)$ is on the graph. However, if the point $(7,0)$ actually is on the graph (rather than $(7−9^{−2},0)$), then $y$ isn't $2+\log_9(7−x)\ldots$