Question

If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$ then the value $xyz$ is

• A. $0$
• B. $1$
• C. $2$
• D. None

Answer 1

Answer: (B)

$1$

Let, $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}=k$

$\log x=k(b-c),\log y=k(c-a),\log z=k(a-b)$

$\log x+\log y+\log z=k(b-c)+k(c-a)+k(a-b)$

$\Rightarrow \log \left(xyz\right)=kb-kc+kc-ka+ka-kb$

$\Rightarrow \log \left(xyz\right)=0$

$\Rightarrow xyz=1$

Hence, B is the correct option.