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The value of N=((log)5 250)/((log)(50)5)...

The value of `N=((log)_5 250)/((log)_(50)5)-((log)_5 10)/((log)_(1250)5)` is...........

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The correct Answer is:
2
` N = (log_(5)250)/(log_(50)5)-(log_(5)10)/(log_(1250)5)`
` = (log_(5)250)(log_(5)50)-(log_(5)10)(log_(5)1250)`
` = (3+log_(5)2)(2+log_(5)2)-(1+log_(5)2)xx(4+log_(5)2)`
` = (log_(5)2)^(2)+5 log_(5)2+6-[(log_(5)2)^(2)+5 log_(5)2 + 4]`
= 2
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