LetSn be the partial sums of ?-mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(Sn/sn) converges almost surely to ?-88f(x)dF(x). We also obtain strong approximation forH(n)=?k=1nk-1f(Sk/sk)=logn ?-88f(x)dF(x) which will imply the asymptotic normality ofH(n)/log1/2n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for ?-mixing random variables.