A4. Which of the following statements is correct?
(A) $\log 0=0$
(B) $\log 5=\log 10-\log 5$
(C) $10^{\log \pi}=\pi$
(D) $\log 1=1$
(E) If $0<x<y$, then $\log _{\frac{1}{2}} x<\log _{\frac{1}{2}} y$
A4. The statement $\log 0=0$ is incorrect, as the logarithmic function does not have a value at the point 0. The statement $\log 5=\log 10-\log 5$ is also incorrect, since $\log 10-\log 5=\log \frac{10}{5}=\log 2$. The statement $10^{\log \pi}=\pi$ is correct, as on the left side of the equation, the exponential and logarithmic functions with the same bases appear. The statement $\log 1=1$ is incorrect, as $\log 1=0$. If the base of the logarithm is less than 1, the corresponding logarithmic function is decreasing, so statement (E) is also incorrect.