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The reciprocal of 2/((log)4(2000)^6)+3/(...

The reciprocal of `2/((log)_4(2000)^6)+3/((log)_5(2000)^6)` is ............

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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.
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