The reciprocal of 2log4⁡(2000)6+3log5⁡(2000)6 is

N=2logx⁡4+3logx⁡5; where x=(2000)6    =logx⁡42+logx⁡53=logx⁡42⋅53=log(2000)6⁡(2000)=16Hence, the reciprocal of given value is 6.