To express $\log_x 2yz$ as a sum of logarithms, we can use the properties of logarithms, specifically:

1. Product Rule:
   $\log_a (MN) = \log_a M + \log_a N$

Applying the rule to $\log_x 2yz$, we break it down step by step:

$\log_x 2yz = \log_x 2 + \log_x y + \log_x z$

Thus, the correct answer is:

D. $\log_x 2 + \log_x y + \log_x z$

Would you like more explanation or examples?

5 Related Questions:

1. How would you express $\log_x (3ab)$ as a sum of logarithms?
2. Can you simplify $\log_x (pqr^2)$ using logarithm properties?
3. What is the product rule for logarithms, and how does it relate to division?
4. How do logarithm rules apply when variables have exponents (e.g., $\log_x (y^2z^3)$)?
5. What is the difference between $\log_x (M+N)$ and $\log_x (MN)$?

Tip:

Always verify whether you're applying the correct logarithmic property—addition, multiplication, or exponentiation—to avoid common mistakes!