The function $f(x)=\int\limits_0^x \frac{d t}{t}$ satisfies

$f(x+y)=f(x)+f(y)$ $f\left(\frac{x}{y}\right)=f(x)+f(y)$ $f(x y)=f(x)+f(y)$ None of these

$f(x y)=f(x)+f(y)$

$f(x)=\int\limits_0^x \frac{d t}{t}=\log x$ $\Rightarrow f(x y)=\log (x y)=\log x+\log y=f(x)+f(y)$ Hence (3) is the correct answer.