Given log 2 x = m and log 5 y = n. (i) Express 2 m - 3 in terms of x. (ii) Express 5 3n + 2 in terms of y.

Given, ⇒ log 2 x = m and log 5 y = n ⇒ x = 2 m ......(1) and, ⇒ y = 5 n .......(2) (i) Given, ⇒ 2 m - 3 ⇒ 2 m .2 -3 ⇒ Substituting value of x from equation (1) in above equation, we get : ⇒ . Hence, 2 m - 3 = . (ii) Given, ⇒ 5 3n + 2 ⇒ (5 n ) 3 .5 2 Substituting value of 5 n from equation (2) in above equation, we get : ⇒ 25y 3 Hence, 5 3n + 2 = 25y 3 .