The expression in the image appears to be:

$\log_2 4 + \log_2 \sqrt{2}$

Let's solve it step by step.

Step 1: Simplify $\log_2 4$

The base-2 logarithm of 4 can be written as:

$\log_2 4 = \log_2 (2^2) = 2$

Step 2: Simplify $\log_2 \sqrt{2}$

The square root of 2 can be expressed as $2^{1/2}$. Using logarithmic properties:

$\log_2 \sqrt{2} = \log_2 (2^{1/2}) = \frac{1}{2} \cdot \log_2 2$

Since $\log_2 2 = 1$, we have:

$\log_2 \sqrt{2} = \frac{1}{2}$

Step 3: Add the results

Now, combine the simplified terms:

$\log_2 4 + \log_2 \sqrt{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$

Final Answer:

$\log_2 4 + \log_2 \sqrt{2} = \frac{5}{2}$

Would you like further clarification or details about the steps? Here are some related questions:

1. What are the basic properties of logarithms?
2. How do you simplify logarithms with fractional exponents?
3. Can logarithms with different bases be converted into the same base?
4. What is the relationship between logarithms and exponents?
5. How are logarithmic functions used in real-world applications?

Tip: When dealing with logarithms, always check if you can simplify the argument using exponent rules!