Question

prove logx×logy=logx+logy​

Answer 1

Step-by-step explanation:

Let. log x = m

then x = e^m……………………(1)

and log y = n

then y = e^n……………………..(2)

Multiplying eqn. (1) and (2)

x.y = e^m×e^n

or. x.y= e^(m+n)

log ( x.y) = m+n

Putting m =log x. and n= log y

or. log (x.y) = log x + log y. Proved.