Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
-$\log _ { 3 } \left( \frac { x y } { 4 } \right)$
A) $\left( \log _ { 3 } x \right) \left( \log _ { 3 } y \right) \div \log _ { 3 } 4$
B) $\log _ { 3 } x + \log _ { 3 } y + \log _ { 3 } 4$
C) $\log _ { 3 } x + \log _ { 3 } y - \log _ { 3 } 4$
D) $\left( \log _ { 3 } x \right) ^ { 2 } + \left( \log _ { 3 } y \right) ^ { 2 } - \log _ { 3 } 4$

Question

Quizplus · Accepted Answer

Using the quotient and product rules for logarithms, we can rewrite the expression as:
$$\log_3\left(\frac{x}{4}\right)+\log_3(y)$$
Then, using the quotient rule again, we get:
$$\log_3(x)-\log_3(4)+\log_3(y)$$
Simplifying further gives:
$$\log_3(x)+\log_3(y)-\log_3(4)$$
Therefore, the answer is (C).

Rewrite in Terms of Two or More Logarithms Using the Quotient