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2014-07-27T15:18:05+05:30

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Assume that all logarithms are with respect to the same .
Y  =  5 log 2 + 3/2 log 25  + 1/2  log 49 – log 28

We know        log  x  + log y  = log x y       rule 1
       and    n log x = x^n          rule 2 Apply rule 1 on each of the four terms on RHS .
Y = log 25  + log (5²2)3/2  +  log (7²2)1/2  - log 7*2²2               Now apply 1st rule   
   =  log   2^5 * (5²)^3/2  * (7²2)^1/2  / 7*2²      =  log  2^5 * 5^3 * 7 * 7^-1 * 2^-2 

    = log 8 * 125    =  log 1000 = 3


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