Question

x=log( a)bc , y=log (b)ca and z =log( c)ab prove that x+y+z = xyz - z

Answer 1

Given :

$x = log(a) bc \: \: \: \: \: \: \: \: \\ y = log(b) ac \\ z = log(c) ab$
To Find:
$x + y + z = xyz - z$
Solution :
$log(a) bc + log(b) ac + \\ log(c) ab = ( log(a) bc) \\ ( log(b) ac)( log(c) ab) \\ - ( log(c) ab) \\ = xyz - z$
hence proved