To evaluate $\log_2(11)$ using the change-of-base formula, we apply the formula:

$\log_a(b) = \frac{\log_c(b)}{\log_c(a)}$

For this specific question:

$\log_2(11) = \frac{\log(11)}{\log(2)}$

Steps:

1. Use the common logarithm (base 10) or natural logarithm (base $e$) for computation.

2. Compute $\log(11)$ and $\log(2)$ using a calculator:

   • $\log(11) \approx 1.0414$
   • $\log(2) \approx 0.3010$

3. Divide the results: $\frac{\log(11)}{\log(2)} = \frac{1.0414}{0.3010} \approx 3.4594$

Final Answer:

$\log_2(11) \approx 3.4594 \quad \text{(rounded to 4 decimal places)}.$

Would you like further clarification or more examples? Let me know!

Here are 5 related questions for deeper understanding:

1. What is the general formula for changing the base of logarithms, and why does it work?
2. How would you compute $\log_2(15)$ using the same method?
3. What are the differences between natural logarithms and common logarithms?
4. How can you verify the accuracy of your calculation using a scientific calculator?
5. Can you solve for $x$ in $2^x = 11$ using logarithms?

Tip: When solving logarithms with non-standard bases, using a calculator's common or natural log functions is the most practical method.