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) $\log _ { a } \frac { q ^ { 5 } f ^ { 1 / 3 } } { r ^ { 5 / 4 } p ^ { 3 } }$

C) $\log _ { a } \frac { q ^ { 5 } r ^ { 5 / 4 } } { f ^ { 1 / 3 } p ^ { 3 } }$

D) $\log _ { a } \left( 5 q - \frac { 5 } { 4 } r + \frac { 1 } { 3 } f - 3 p \right)$

Question

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) $\log _ { a } \frac { q ^ { 5 } f ^ { 1 / 3 } } { r ^ { 5 / 4 } p ^ { 3 } }$

C) $\log _ { a } \frac { q ^ { 5 } r ^ { 5 / 4 } } { f ^ { 1 / 3 } p ^ { 3 } }$

D) $\log _ { a } \left( 5 q - \frac { 5 } { 4 } r + \frac { 1 } { 3 } f - 3 p \right)$

Quizplus · Accepted Answer

The properties of logarithms allow us to combine terms by applying the coefficients as exponents and by understanding that subtraction in terms of logarithms translates to division, while addition translates to multiplication. Therefore, the correct expression is $\log _ { a } \frac { q ^ { 5 } f ^ { 1 / 3 } } { r ^ { 5 / 4 } p ^ { 3 } }$.

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