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?
Solution) 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).