Question

The value of the expression $8{\log }_a{x}^3\cdot {\log }_b{y}^3\cdot {\log }_c{z}^3$, where $a=y^2,b=z^2,c=x^2$ is equal to

Answer 1

$8{\log }_a{x}^3.{\log }_b{y}^3.{\log }_c{z}^3$

$=8.\left(\frac{\log x^3}{\log a}\right).\left(\frac{\log y^3}{\log b}\right).\left(\frac{\log z^3}{\log c}\right)$

$=8.\left(\frac{\log x^3}{\log y^2}\right).\left(\frac{\log y^3}{\log z^2}\right).\left(\frac{\log z^3}{\log x^2}\right)$

$=8.[\frac{3\log x}{2\log y}.\frac{3\log y}{2\log z}.\frac{3\log z}{2\log y}]$

$=8\times \frac{3^3}{2^3}=3^3=27$