Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × œ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °




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Topic review (newest first)

2005-12-15 01:18:04

Call f anything you wish k, n, l, ...  it is not ƒ , a function.

2005-12-15 01:11:45

My post wasn't very clear, so let me first clarify that it is not given that f(Ax) = f(By). I should add that f denotes an activity coefficient, so it's a constant. 

And yes MathsIsFun , A is in base x, and B is in base y. Hope you figure it out cos I've been told it's a difficult problem.

Thank you for your time.

2005-12-14 18:51:45

Ahhh... bases! A is in base x, and B is in base y, right?

2005-12-14 14:57:15

a^x*a^y = a^(x+y), but it only works for a common base. Therefore,

ƒ(AxBy) = ƒ(Ax) * ƒ(By) = [ƒ(Ax) * ƒ(By)]^[(x+y)(1/x+y)] = [ƒ(Ax)^x * ƒ(By)^y]^[1/(x+y)]
if and only if ƒ(Ax) = ƒ(By).

2005-12-14 12:13:45

Can anyone prove the validity of this equation by deriving it :

f(AxBy) = (fA^x•fB^y)^[1/(x+y)]  ?

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