GWD-31-2

Q2:

The function f is defined for each positive three-digit integer n by f(n) = 2^x 3^y 5^z, where x, y, and z are the hundreds, tens, and units digits of n, respectively.  If m and v are three-digit positive integers such that f(m) = 9 f(v), then m - v =

A.      8

B.      9

C.      18

D.     20

E.      80

设 m为x1y1z1,v为x2y2z2

做到2^(x1-x2)3^(y1-y2)5^(z1-z2)=9  就不会做下去了

望高人赐教

f(m) = 9 f(v)

假设f(v)=2^x 3^y 5^z,则f(m)=9f(v)=9*2^x 3^y 5^z   =2^x 3(y+2)5^z 

^{（上面y+2为次方，我不知道怎么打，楼主，怎么打上去得，请指教）}

^{所以m是一个十位上比n大2得三位数，所以差为20}