Question

If $\frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}$,show that $xyz=1$

Answer 1

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

$\log x=k(b-c)$

$x={10}^{k(b-c)}$

$y={10}^{k(c-a)}$

$z={10}^{k(a-b)}$

$xyz={10}^{k(b-c+c-a+a-b)}$

$={10}^0$

$=1$