The reciprocal of `2/(log_(4)(2000)^(6))+3/(log_(5)(2000)^(6))` is _______.

Answer

6

Explanation

Let `N = 2 log_(x) 4+3 log_(x) 4+3 log_(x) 5," where " x = (2000)^(6)`
` = log_(x) 4^(2) + log_(x) 5^(3)`
` = log_(x) 4^(2) * 5^(3) `
` = log_(x) 4^(2) * 5^(3) `
` = log_((2000)^(6))(2000)`
` = 1/6`
Hence, the reciprocal of given value is 6.