Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$4 \log _{c} q-\frac{2}{5} \log _{c} r+\frac{1}{6} \log _{c} f-6 \log _{c} p$

A) $\log _{c} \frac{q^{4} r^{2 / 5}}{f^{1 / 6} p^{6}}$

B) $\log _{c} \frac{q^{4} f^{1 / 6}}{r^{2 / 5} p^{6}}$

C) $\log _{c}\left(4 q-\frac{2}{5} r+\frac{1}{6} f-6 p\right)$

D) $\log _{c} \frac{q^{4} p^{6}}{f^{1 / 6} r^{2 / 5}}$

Question

Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable expressions are positive and bases are positive numbers not equal to 1 .
-$4 \log _{c} q-\frac{2}{5} \log _{c} r+\frac{1}{6} \log _{c} f-6 \log _{c} p$

A) $\log _{c} \frac{q^{4} r^{2 / 5}}{f^{1 / 6} p^{6}}$

B) $\log _{c} \frac{q^{4} f^{1 / 6}}{r^{2 / 5} p^{6}}$

C) $\log _{c}\left(4 q-\frac{2}{5} r+\frac{1}{6} f-6 p\right)$

D) $\log _{c} \frac{q^{4} p^{6}}{f^{1 / 6} r^{2 / 5}}$

Quizplus · Accepted Answer

The properties of logarithms allow us to combine terms by converting multiplication into addition and division into subtraction, and powers are handled by multiplying the logarithm by the exponent. The correct combination is $\log _{c} \frac{q^{4} f^{1 / 6}}{r^{2 / 5} p^{6}}$, which matches option B.

Rewrite the Given Expression as a Single Logarithm 4log⁡cq−25log⁡cr+16log⁡cf−6log⁡cp4 \log _{c} q-\frac{2}{5} \log _{c} r+\frac{1}{6} \log _{c} f-6 \log _{c} p4logc​q−52​logc​r+61​logc​f−6logc​p

Rewrite the Given Expression as a Single Logarithm $4 \log _{c} q-\frac{2}{5} \log _{c} r+\frac{1}{6} \log _{c} f-6 \log _{c} p$