we
have
x=
log_a(bc)
so
1 + x = 1 + log_a(bc) = log_a(a) + log_a(bc) = log_a(abc)
or
\dfrac{1}{1+x} = log_{abc}(a) \cdots (1)
similarly
\dfrac{1}{1+y} = log_{abc}(b) \cdots (2)
\dfrac{1}{1+z} = log_{abc}(c) \cdots (3)
\dfrac{1}{1+x}+ \dfrac{1}{1+y}+ \dfrac{1}{1+z} = log_{abc}(a) + log_{abc}(b) + log_{abc}(c) = log_{abc}(abc) = 1
or
(1+y)(1+z) + (1+z)(1+x) + (1+x)(1+y) = (1+x)(1+y)(1+ z)
or
1 + yz + y + z + 1 + xz + x + z + 1 + xy + x + z = 1 + x + y + z + xy + yz + zx + xyz
or 2 + x + y+ z = xyz
or xyz – x – y -z = 2
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