Question

Prove that logxy= logx+logy

Answer 1

Answer:

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.

If a is the base of the logarithm, then raise both the sides separately to the exponent on a. Applying the rule of indices we get both sides as xy as by definition of logarithm of x to the base 'a’, we have a^(log_a)(x) =x. Thereafter we can conclude the result from the injectivity of the power function.

Alternatively a^(RHS) = xy ==> RHS=(log_a)(xy)

Step-by-step explanation:

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