標題:

Maths

發問:

If 2^x = 3^y = 12^z Show that xy = z( x+ 2y)

最佳解答:

2^x = 3^y = 12^z x log2 = y log3 = z log12 = K (where K is a constant) So, x = K/log2, y = K/log3, z = K/log12 xy = K^2/[(log2)(log3)] z(x + 2y) = (K/log12)(K/log2 + 2K/log3) = (K/log12)[(log3)K + (2log2)K]/[(log2)(log3)] = (K/log12)[K(log3 + 2log2)]/[(log2)(log3)] = K^2/[(log2)(log3)] So xy = z(x + 2y)

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