Question

Prove that :  (log a)² - (log b)² = log ${\displaystyle \left(\frac{a}{b}\right)}$ . Log (ab)

Answer 1

L.H.S = ( log a )²  - ( log b  )² 

⇒ L.H.S = ( log a + log b ) ( log a - log b )

⇒ L.H.S = log ( ab ) log ${\displaystyle \left(\frac{a}{b}\right)}$

⇒ L.H.S = log ${\displaystyle \left(\frac{a}{b}\right)}$ x log ( ab) 

⇒ L.H.S = R.H.S

Hence proved.