To find the approximate value of \(\log_2 10\), we can use the given information that \(2^{10} \approx 10^3\). Here's how you can calculate it:

1. Use the given approximation:
\[
2^{10} \approx 10^3
\]

2. Take the logarithm base 10 of both sides:
\[
\log_{10}(2^{10}) \approx \log_{10}(10^3)
\]

3. Simplify the logarithms:
\[
10 \log_{10} 2 \approx 3
\]
\[
\log_{10} 2 \approx \frac{3}{10}
\]

4. Convert the logarithm base 10 to base 2:
\[
\log_2 10 = \frac{\log_{10} 10}{\log_{10} 2} = \frac{1}{\log_{10} 2}
\]
\[
\log_2 10 \approx \frac{1}{\frac{3}{10}} = \frac{10}{3}
\]

So, the approximate value of \(\log_2 10\) is \(\frac{10}{3}\). The correct answer is:

A. \(\frac{10}{3}\)