If $x = l o g_{b} a, y = l o g_{c} b, z = l o g_{a} c$ , then xyz is

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None of these

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Solution

The correct option is B 1
We have $x y z = l o g_{b} a \times l o g_{c} b \times l o g_{a} c = \frac{l o g_{e}}{l o g_{e} b} \times \frac{l o g_{e} b}{l o g_{e} c} \times \frac{l o g_{e} c}{l o g_{e} a} = 1.$

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Similar questions

x = l o g_{b} a, y = l o g_{c} b, z = l o g_{a} c

l o g_{c} b + l o g_{b} c

y = l o g_{a} c + l o g_{c} a,

z = l o g_{b} a + l o g_{a} b

x y z = x^{2} + y^{2} + z^{2} - 4.

\frac{1}{1 + {log}_{b} a + {log}_{b} c} + \frac{1}{1 + {log}_{c} a + {log}_{c} b} + \frac{1}{1 + {log}_{a} b + {log}_{a} c}

{log}_{b} a + {log}_{c} a + {log}_{a} b + {log}_{a} c + {log}_{b} c + {log}_{c} b = 3

a, b, c

\neq 1

a b c

\frac{1}{1 + {log}_{b} a + {log}_{b} c} + \frac{1}{1 + {log}_{c} a + {log}_{c} b} + \frac{1}{1 + {log}_{a} b + {log}_{a} c}

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