Question

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

Answer 1

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

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

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

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

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

$x^a{y}^b{z}^c={10}^{k(b-c)a}\times {10}^{k(c-a)b}\times {10}^{k(a-b)c}$

$={10}^{k(ab-ac+bc-ab+ac-bc)}$

$={10}^0$

$=1$