Express as a single logarithm.
-$$5 \log _ { a } q - \frac { 5 } { 4 } \log _ { a } r + \frac { 1 } { 3 } \log _ { a } f - 3 \log _ { a } p$$
A) $\log _ { a } \frac { q ^ { 5 } p ^ { 3 } } { f ^ { 1 / 3 } r ^ { 5 / 4 } }$
B) $\log _ { a } \frac { q ^ { 5 } \mathrm { f } ^ { 1 / 3 } } { r ^ { 5 / 4 } p ^ { 3 } }$
C) $\log _ { a } \frac { q ^ { 5 } r ^ { 5 / 4 } } { f ^ { 1 / 3 } p ^ { 3 } }$
D) $\log _ { \mathrm { a } } \left( 5 \mathrm { q } - \frac { 5 } { 4 } \mathrm { r } + \frac { 1 } { 3 } \mathrm { f } - 3 \mathrm { p } \right)$

Question

Quizplus · Accepted Answer

The expression can be combined using the properties of logarithms: $5 \log_a q$ becomes $\log_a q^5$, $-\frac{5}{4} \log_a r$ becomes $\log_a r^{-5/4}$, $\frac{1}{3} \log_a f$ becomes $\log_a f^{1/3}$, and $-3 \log_a p$ becomes $\log_a p^{-3}$. Combining these gives $\log_a \frac{q^5 f^{1/3}}{r^{5/4} p^3}$.

Express as a Single Logarithm 5log⁡aq−54log⁡ar+13log⁡af−3log⁡ap5 \log _ { a } q - \frac { 5 } { 4 } \log _ { a } r + \frac { 1 } { 3 } \log _ { a } f - 3 \log _ { a } p5loga​q−45​loga​r+31​loga​f−3loga​p

Express as a Single Logarithm $5 \log _ { a } q - \frac { 5 } { 4 } \log _ { a } r + \frac { 1 } { 3 } \log _ { a } f - 3 \log _ { a } p$