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# When n = 100x + 10y + z, function f is defined as f(n) =

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Joined: 25 Nov 2004
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Kudos [?]: 122 [0], given: 0

When n = 100x + 10y + z, function f is defined as f(n) = [#permalink]

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22 Jun 2006, 21:46
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When n = 100x + 10y + z, function f is defined as f(n) = (2^x)(3^y)(5^z). If f(v) = 9f(u), what is v minus u?

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Intern
Joined: 04 May 2006
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22 Jun 2006, 23:39
20 it is.

Suppose u = 100 x1+10 y1+z1
and v = 100 x2+10 y2+z2
So F(u) = 2 ^ x1 * 3 ^ y1 * 5^ z1 and
F(v) = 2 ^ x2 * 3 ^ y2 * 5^ z2

F(v) = 9 F(u) =>
2 ^ x2 * 3 ^ y2 * 5^ z2 = 9 * 2 ^ x1 * 3 ^ y1 * 5^ z1
That gives x2 = x1, y2 = y1+2, z2 = z1.

Now if we subtract u from v, we get 20.
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22 Jun 2006, 23:39
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# When n = 100x + 10y + z, function f is defined as f(n) =

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