Value of `[2/((log)_4(2000)^6)+3/((log)_5(2000)^6)]` is `4^(1/3). 5^(1//2)` b. `1/6` c. `3 3` d. none of these

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.