Let's work through the problems step-by-step. Here’s a solution guide for each logarithmic expression:

(a) $\log_{10} 1000$

The formula for logarithms is $\log_b(x) = y$ if $b^y = x$.
Since $10^3 = 1000$, the answer is:
$\log_{10} 1000 = 3$

(b) $\log_{4} 2$

This asks for $4^y = 2$. Rewriting 4 as $2^2$,
$(2^2)^y = 2 \implies 2^{2y} = 2^1 \implies 2y = 1 \implies y = \frac{1}{2}$
Thus, $\log_{4} 2 = \frac{1}{2}$.

Would you like me to proceed with all parts, or do you want a specific one explained next? Let me know!

Here are 5 questions for expanding understanding:

1. How does the change of base formula help in logarithmic calculations?
2. Why is $\log_b(b) = 1$ a useful property?
3. How do negative bases affect logarithmic results?
4. What are some real-world applications of logarithms?
5. How can you simplify products or sums involving logarithms?

Tip: Always check if the base and argument can be expressed in terms of the same power. It simplifies solving significantly!