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Let L denote antilog32 0.6 and M denote ...

Let `L` denote antilog_32 0.6 and M denote the number of positive integers which have the characteristic 4, when the base of log is 5, and N denote the value of `49^((1-(log)_7 2))+5^(-(log)_5 4.)` Find the value of `(L M)/Ndot`

Text Solution

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`L="antilog"_(32)0.6=(32)^(6//10) = 2^((5xx6)//10)=2^(3) = 8`
M = Integer from 625 to 3125 = 2500
`N = 49^(1-log_(7)2)+5^(-log_(5)4)`
` = 49 xx 7^(-2 log_(7)2)+5^(-log_(5)4)`
` 49 xx 1/4+1/4=50/4 = 25/2`
`:. (LM)/N = (8xx2500xx2)/25 = 1600`
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