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Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve y=log2(12x-96). What is the value of m+n?
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we have x''''=x+m =>m=x''''-xand y'''' =y+n =>n=y''''-yhence m+n=(x''''+y'''') - (x+y)taking y''''=y=1 we get m+n= x''''-xputting y=1 in y=log2 3x.... we get x=2/3putting y''''=1 in y''''=log2 (12x''''-96)... we get x''''=49/6Hence m+n= x''''-x=49/6 - 2/3 =45/6=15/2hence m+n= 15/2 (ANS).
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