21. Let $f$ be a function so that
$$
f(x)-\frac{1}{2} f\left(\frac{1}{x}\right)=\log x
$$
for all $x>0$, where log denotes logarithm base 10 . Find $f(1000)$.
21. Ans: 2
Putting $1 / x$ in place of $x$ in the given equation yields
$$
f\left(\frac{1}{x}\right)-\frac{1}{2} f(x)=-\log x .
$$

Solving for $f(x)$, we obtain $f(x)=\frac{2}{3} \log x$. Hence $f(1000)=2$.