Use the properties of logarithms to expand the expression as a sum,difference,and/or constant multiple of logarithms.(Assume all variables are positive. )? $\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }$ ? A)3log₈ x + 3log₈ y + 3log₈ z B)3log₈ x + 3log₈ y - 3log₈ z C) $\frac { 3 \log _ { 8 } x } { 3 \log _ { 8 } y \times 3 \log _ { 8 } z }$ D)3log₈ x - 3log₈ y - 3log₈ z E)3log₈ x - 3log₈ y + 3log₈ z

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\log _ { 8 } \frac { x ^ { 3 } } { y ^ { 3 } z ^ { 3 } }$ can be expanded as $3\log_8 x - 3\log_8 y - 3\log_8 z$. This uses the property that $\log_b \frac{M}{N} = \log_b M - \log_b N$ and the power rule $\log_b M^k = k\log_b M$.

Use the Properties of Logarithms to Expand the Expression as a Sum,difference,and/or