This question was uploaded on 27/10/21 on social media accounts.
Symmetrical equations with three variables based on logarithm.
Solution:
\[\frac{\log x}{b-c}=\frac{\log y}{c-a}\]
\[\Rightarrow\color{blue} {x^{c-a}=y^{b-c}}----(1)\]
Similarly:
\[\Rightarrow\color{fuchsia} {y^{a-b}=z^{c-a}}----(2)\]
\[\Rightarrow\color{red} {z^{b-c}=x^{a-b}}----(3)\]
Multiplying all three equations:
\[x^{c-a} \cdot y^{a-b} \cdot z^{b-c} = y^{b-c} \cdot z^{c-a} \cdot x^{a-b}\]
\[\Rightarrow x^{2a} \cdot y^{2b} \cdot z^{2c} = x^{b+c} \cdot y^{c+a} \cdot z^{a+b}\]
\[\Rightarrow \frac{x^{2a} \cdot y^{2b} \cdot z^{2c}}{x^{b+c} \cdot y^{c+a} \cdot z^{a+b}} = 1\]
Question based on Algebra, Ratio, Equation.
