Question

Prove that $\log \frac{65}{19}+\log \frac{133}{143}+\log \frac{11}{35}=0$

Answer 1

Apply property- $\log (a\times b)=\log a+\log b$

$\log \frac{65}{19}+\log \frac{133}{143}+\log \frac{11}{35}$

$=\log (\frac{65}{19}\times \frac{133}{143}\times \frac{11}{35})$

$=\log (\frac{65}{1}\times \frac{7}{143}\times \frac{11}{35})$

$=\log (\frac{65}{1}\times \frac{1}{13}\times \frac{1}{5})$

$=\log 1$

$=0$