Good Day,

We know these facts:

$\displaystyle x = log_a(bc)$

$\displaystyle y = log_b(ca)$

$\displaystyle z = log_c(ab)$

The equation below must be proved:

$\displaystyle x + y + z + 2 = xyz$

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- Feb 1st 2011, 09:45 PMmehdiHow do you prove this?
Good Day,

We know these facts:

$\displaystyle x = log_a(bc)$

$\displaystyle y = log_b(ca)$

$\displaystyle z = log_c(ab)$

The equation below must be proved:

$\displaystyle x + y + z + 2 = xyz$ - Feb 2nd 2011, 12:04 AMsimplependulum
Consider

$\displaystyle bc = a^x ~,~ ca = b^y ~,~ ab=c^z $ we have

$\displaystyle a^{xyz} = (bc)^{yz} = (b^y)^z (c^z)^y = (ca)^z (ab)^y = a^{z+y} b^y c^z = a^{z+y} (ca)(ab) = a^{2+z+y} bc = a^{x+y+z+2} $

Thus , $\displaystyle xyz = x+y+z+2 $