Write as a single logarithm. Assume that variables represent positive numbers.

To combine \( 4 \log_2 x + 2 \log_2 z \) into a single logarithm, we can use the properties of logarithms.

1. Use the power rule: \( a \log_b c = \log_b (c^a) \).
- For \( 4 \log_2 x \), we can write it as \( \log_2 (x^4) \).
- For \( 2 \log_2 z \), we can write it as \( \log_2 (z^2) \).

Now we have:
\[
\log_2 (x^4) + \log_2 (z^2)
\]

2. Use the product rule: \( \log_b a + \log_b c = \log_b (a \cdot c) \).
- Combining the two logarithms gives us:
\[
\log_2 (x^4 \cdot z^2)
\]

Thus, the expression \( 4 \log_2 x + 2 \log_2 z \) can be expressed as a single logarithm:
\[
\log_2 (x^4 z^2)
\]

So the final answer is:
\[
\log_2 (x^4 z^2)
\]