Question

Show that $\frac{{\log }_{a}x}{{\log }_{a}y}=\frac{{\log }_{b}x}{{\log }_{b}y}$

Answer 1

Consider, $\frac{{\log }_{a}x}{{\log }_{a}y}$

$={\log }_{y}x$

Changing to base $b$

$=\frac{{\log }_{b}x}{{\log }_{b}y}$
Base can be any positive quantity but not equal to $1.$