Question

I$fx=lo{g}_{7}9,y=lo{g}_{5}7,z=lo{g}_{3}5$ show that $xyz=2$.

Answer 1

We can write $x=\frac{\log 9}{\log 7}y=\frac{\log 7}{\log 5}z=\frac{\log 5}{\log 3}$

Now, $xyz=\frac{\log 9}{\log 7}\frac{\log 7}{\log 5}\frac{\log 5}{\log 3}=\frac{\log 9}{\log 3}={\log }_{3}9={\log }_3{3}^2=2{\log }_{3}3=2$