Graphing problem?

[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 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)

 

So could someone please tell me how to graph it? I have a "Texas Instruments Ti-nspire CAS" if that helps

Thanks alot.