Let $H(X)$ denote the entropy of a discrete random variable $X$ taking $K$ possible distinct real values. Which of the following statements is/are necessarily true?

- $H(X) \leq \log_{2} K \; \text{bits}$
- $H(X) \leq H (2X)$
- $H(X) \leq H (X^{2})$
- $H(X) \leq H (2^{X})$