Question

$\lim_{x \to \02} log_2 \sqrt{x}$

Answer 1

$\displaystyle L=\lim\limits_{x\to2}\frac{1}{2}\log_2 x\\ \\ L=\frac{1}{2}\lim\limits_{x\to2}\log_2 x\\ \\ \text{Por la continuidad de Log}: \\ \\ L=\frac{1}{2}\log_2\left(\lim\limits_{x\to2} x\right)\\ \\ L=\frac{1}{2}\log_22\\ \\ \boxed{L=\frac{1}{2}}$