Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$
A) $6 \log _ { 3 } y - 2 \log _ { 3 } x$
B) $2 \log _ { 3 } x + 6 \log _ { 3 } y$
C) $\frac { 1 } { 3 } \log _ { 3 } \left( \frac { x } { y } \right)$
D) $2 \log _ { 3 } x - 6 \log _ { 3 } y$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression can be rewritten as the difference of the logarithms of the numerator and denominator, with the exponents factored out: $\log_3(x^2) - \log_3(y^6) = 2\log_3(x) - 6\log_3(y)$.

Write as the Sum And/or Difference of Logarithms log⁡3(x2y6)\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)log3​(y6x2​)

Write as the Sum And/or Difference of Logarithms $\log _ { 3 } \left( \frac { x ^ { 2 } } { y ^ { 6 } } \right)$