Problem
Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. \[ \log _{3}\left(\frac{4 y}{z}\right) \] Choose the correct answer. A. This cannot be simplified. B. $\log _{3} 4+\log _{3} y \div \log _{3} z$ C. $\log _{3} 4 \cdot \log _{3} y \div \log _{3} z$ D. $\log _{3} 4+\log _{3} y-\log _{3} z$
Solution
Step 1 ：Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
Step 2 ：\(\log _{3}\left(\frac{4 y}{z}\right)\)
Step 3 ：Choose the correct answer.
Step 4 ：Final Answer: \(\boxed{\text{D. } \log _{3} 4+\log _{3} y-\log _{3} z}\)
