Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
-$$\log _ { 3 } \left( \frac { x ^ { 8 } y ^ { 4 } } { 6 } \right)$$
A) $\left( 8 \log _ { 3 } x \right) \left( 4 \log _ { 3 } y \right) \div \log _ { 3 } 6$
B) $8 \log _ { 3 } x + 4 \log _ { 3 } y - \log _ { 3 } 6$
C) $8 \log _ { 3 } x + 4 \log _ { 3 } y + \log _ { 3 } 6$
D) $\left( \log _ { 3 } x \right) ^ { 8 } + \left( \log _ { 3 } y \right) ^ { 4 } - \log _ { 3 } 6$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression can be rewritten as the sum of the logs of the numerator's components minus the log of the denominator. This simplifies to $8 \log _ { 3 } x + 4 \log _ { 3 } y - \log _ { 3 } 6$.

Use the Properties of Logarithms to Rewrite the Expression log⁡3(x8y46)\log _ { 3 } \left( \frac { x ^ { 8 } y ^ { 4 } } { 6 } \right)log3​(6x8y4​)

Use the Properties of Logarithms to Rewrite the Expression $\log _ { 3 } \left( \frac { x ^ { 8 } y ^ { 4 } } { 6 } \right)$