TheAlchemist

I'm trying to learn more about the Lac operon, and I am confused regarding a few thing. (sorry if this is the wrong section) IPTG is a known inducer of the lac operon, which can be used instead of allolactose. My question regarding IPTG is as follows; does IPTG lead to transcription of the Lac operon or only the removal of the lac repressor? Because as I understand it, cAMP is needed as well, in order to bind the CAP activator to the CAP-binding site, so that RNA Polymerase can be recruited to the operon. So if I had glucose and IPTG, would the operon still be transcribed, since glucose leads to decrease in cAMP concentration. The second question is regarding Glycerol; if it is used instead of lactose, would I still have transcription of the lac operon? Since there is no inducer to bind to the lac repressor, with glycerol I only have cAMP, is that enough? Thank you in advance for all the help!