Write the expression as the sum or difference of single logarithms.
-$\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$
A) $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - 2 \log _ { 10 } y$
B) $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } y$
C) $3 \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } 3$
D) $\log _ { 10 } 17 - \log _ { 10 } x - \log _ { 10 } y$

Question

Quizplus · Accepted Answer

The expression $\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$ can be broken down using logarithm properties: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$, the power rule $\log_b M^k = k \log_b M$, and the root rule which is a specific case of the power rule, $\log_b \sqrt[k]{M} = \frac{1}{k} \log_b M$. Applying these rules, we get $\frac { 1 } { 3 } \log _ { 10 } 17 - 2 \log _ { 10 } x - \log _ { 10 } y$.

Write the Expression as the Sum or Difference of Single log⁡10(173x2y)\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)log10​(x2y317​​)

Write the Expression as the Sum or Difference of Single $\log _ { 10 } \left( \frac { \sqrt [ 3 ] { 17 } } { x ^ { 2 } y } \right)$