Expand. Assume that all variables represent positive real numbers.
-$\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)$
A) $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c + 6$
B) $7 \log _ { d } a + 5 \log _ { d } b - 3 \log _ { d } c - 6$
C) $\log _ { \mathrm { d } } \mathrm { a } ^ { 7 } + \log _ { \mathrm { d } } \mathrm { b } ^ { 5 } + \log _ { \mathrm { d } } \mathrm { c } ^ { 3 } - \log _ { \mathrm { d } } \mathrm { b } ^ { 6 }$
D) $a ^ { 7 } b ^ { 5 } - c ^ { 3 } d ^ { 6 }$

Question

Quizplus · Accepted Answer

Using the logarithm properties, the expression can be expanded as follows: $\log_d(a^7) + \log_d(b^5) - \log_d(c^3) - \log_d(d^6)$. This simplifies to $7\log_d(a) + 5\log_d(b) - 3\log_d(c) - 6$, because $\log_d(d^6) = 6\log_d(d) = 6$, since $\log_d(d) = 1$.

Expand Assume That All Variables Represent Positive Real Numbers log⁡d(a7b5c3d6)\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)logd​(c3d6a7b5​)

Expand Assume That All Variables Represent Positive Real Numbers $\log _ { d } \left( \frac { a ^ { 7 } b ^ { 5 } } { c ^ { 3 } d ^ { 6 } } \right)$