Expand. A ssume that all variables represent positive real numbers.
-$\log _{7}\left(\frac{12 \sqrt{\mathrm{r}}}{\mathrm{s}}\right)$
A) $\log _{7} 12 \cdot \frac{1}{2} \log _{7} \mathrm{~m} \div \log _{7} \mathrm{~s}$
B) $\log _{7}(12 \sqrt{r})-\log _{7} s$
C) $\log _{7} \mathrm{~s}-\log _{7} 12-\frac{1}{2} \log _{7} \mathrm{r}$
D) $\log _{7} 12+\frac{1}{2} \log _{7} r-\log _{7} s$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we can expand the expression as follows:$\log _{7}\left(\frac{12 \sqrt{\mathrm{r}}}{\mathrm{s}}\right)=\log _{7} 12+\log _{7} \sqrt{\mathrm{r}}-\log _{7} \mathrm{~s}$$\log _{7} 12+\log _{7} \sqrt{\mathrm{r}}-\log _{7} \mathrm{~s}=\log _{7} 12+\frac{1}{2} \log _{7} \mathrm{r}-\log _{7} \mathrm{~s}$

Expand a Ssume That All Variables Represent Positive Real Numbers log⁡7(12rs)\log _{7}\left(\frac{12 \sqrt{\mathrm{r}}}{\mathrm{s}}\right)log7​(s12r​​)

Expand a Ssume That All Variables Represent Positive Real Numbers $\log _{7}\left(\frac{12 \sqrt{\mathrm{r}}}{\mathrm{s}}\right)$