Graphing of Cosine/Logarithm Function

Malinn

I have been given a graph to sketch.
The original graph was:
T= 20-4cos(pi(x-1)/12)
I think I understand how to graph this , but later on they change it to this:
T= 20-loge(x) 4cos(pi(x-1)/12)

What type of graph is that? I don't even know if it exists, as I can't find anything in the textbook. I thought maybe, it would just be the "cos" part of the equation, but that doesn't work as that is the same as the original equation.
I know it must follow the same shape as a log graph would because it asks you to do this after sketching the second graph:

If the cycle starts at midnight Sunday, what day(s) will the temperature of the pool be more than 24.5 degrees celcius? (Just days not times)

This means it has to be a log shaped graph as if it was just the T= 20-4cos(pi(x-1)/12) then the temperature would never reach 24.5 degrees celcius (as themaximum value is 24)

So could someone please tell me how to graph this T= 20-loge(x) 4cos(pi(x-1)/12)? I have a "Texas Instruments Ti-nspire CAS" if that helps
Thanks alot.