We need to evaluate the limit of the function $\log_2(\frac{1}{x})$ as $x$ approaches 0 from the positive side. That is, we want to find $\lim_{x \to 0^+} \log_2(\frac{1}{x})$.

1. Problem Description

We need to evaluate the limit of the function $\log_2(\frac{1}{x})$ as $x$ approaches 0 from the positive side. That is, we want to find $\lim_{x \to 0^+} \log_2(\frac{1}{x})$.

2. Solution Steps

Let's analyze the behavior of the function $\frac{1}{x}$ as $x$ approaches 0 from the positive side ($x \to 0^+$).

As $x$ approaches 0 from the right, $\frac{1}{x}$ approaches positive infinity.

$\lim_{x \to 0^+} \frac{1}{x} = \infty$

Now, consider the logarithm function with base 2, $\log_2(y)$. As $y$ approaches infinity, $\log_2(y)$ also approaches infinity. That is,

$\lim_{y \to \infty} \log_2(y) = \infty$

Replacing $y$ with $\frac{1}{x}$, we have:

$\lim_{x \to 0^+} \log_2(\frac{1}{x}) = \lim_{y \to \infty} \log_2(y) = \infty$

3. Final Answer

$\infty$