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

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Quizplus · Accepted Answer

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

Use the Properties of Logarithms to Expand the Expression as a Sum