how to prove the second law of logarithms?
Answer:
second law of logarithms state that log(a/b) = log(a) - log(b)
(let the base of the logs be c everywhere)
let log(a) be x and log(b) be y
this implies that c^x=a and c^y=b
now (a/b)=(c^x/c^y)
and (c^x/c^y)=(c^x)(c^-y)=(c^x-y)
this implies that log(a/b)=(x-y)
x=log(a) and y=log(b)
therefore log(a/b)=log(a)-log(b)
hence the second law of logarithms is proved
