Let `f: R->R` whre `R^+` is the set of all positive real numbers, be such that `f(x)=(log)_e xdot` Determine: whether `f(x y)=f(x)+f(y)` holds.

Explanation

Here, we have

`f (x) = log_e x ⇒ f (y) = log_e( y)
`Then, let us consider the
f(xy) `F(xy) = log_e(xy)f(xy) = log_e (x × y)`

`=> f(xy) = log_e x + log_e y `

`=>f(xy) = f (x) + f (y)`

Thus the equation `f(xy) = f(x) + f(y)` holds.