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Lactose does not easily diffuse across the E. coli and must be actively transported into the cell by enzyme permease
the enzymes galctosidase, permease and transacetylase are produced in small amount in absence of lactose.
when glucose is utilized and lactose is added synthesis of all the three enzymes increases about thousandfold with in 2 to 3 times.
so with small amount of permease present in cell lactose is diffused across membrane.