This condition in lac operon facilitates the condition of lac genes being transcribed at high levels

The correct option is low glucose, high lactose.

The lac operon is an inducible operon in bacteria (such as Escherichia coli) that regulates the transport and metabolism of lactose. It is controlled by two main regulatory mechanisms that respond to the availability of glucose and lactose in the cell's environment.

Let's break down how these two conditions (low glucose and high lactose) work together to facilitate transcription of the lac genes at high levels:

1. Presence of High Lactose (Inactivation of the Repressor):
Normally, a repressor protein (encoded by the lacI gene) binds to the operator region of the operon and physically blocks RNA polymerase from transcribing the structural genes. When lactose is present in high concentrations, a small amount of it is converted into allolactose. Allolactose acts as an inducer by binding directly to the repressor protein. This binding causes a conformational change in the repressor, making it release from the operator. With the repressor out of the way, the promoter is accessible, allowing transcription to proceed (de-repression).

2. Presence of Low Glucose (Activation of CAP-cAMP Complex):
Glucose is the preferred energy source for E. coli. When glucose levels are high, the cell prevents transcription of alternative sugar pathways. However, when glucose levels are low, the concentration of the intracellular signaling molecule cyclic AMP (cAMP) increases.
cAMP binds to the Catabolite Activator Protein (CAP), also known as cAMP Receptor Protein (CRP). The binding of cAMP to CAP forms an active CAP-cAMP complex. This complex binds to a specific site upstream of the promoter, which significantly enhances the binding affinity of RNA polymerase to the promoter, acting like an accelerator for transcription.

Conclusion:
For the lac operon to be transcribed at high levels, both of the following conditions must be met:
- The "brake" must be released: Lactose must be high to remove the repressor.
- The "accelerator" must be pressed: Glucose must be low to activate the CAP-cAMP complex, which recruits RNA polymerase efficiently.
Therefore, the combination of low glucose and high lactose is the precise condition that facilitates high-level transcription of the lac genes.