Write as the sum and/or difference of logarithms. Express powers as factors.
-$\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }$
A) $\frac { 1 } { 2 } \log _ { 12 } \mathrm { rs } - \frac { 1 } { 2 } \log _ { 12 } 13$
B) $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \log _ { 12 } 13$
C) $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } \cdot \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} + \frac { 1 } { 2 } \log _ { 12 } 13$
D) $\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \frac { 1 } { 2 } \log _ { 12 } 13$

Question

Quizplus · Accepted Answer

The expression $\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }$ can be rewritten using the properties of logarithms: $\frac{1}{2} \log _ { 12 } \mathrm{rs} - \frac{1}{2} \log _ { 12 } 13$. This further breaks down to $\frac{1}{2} (\log _ { 12 } \mathrm{r} + \log _ { 12 } \mathrm{s}) - \frac{1}{2} \log _ { 12 } 13$, which matches option D.

Write as the Sum And/or Difference of Logarithms log⁡12rs13\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }log12​13rs​​

Write as the Sum And/or Difference of Logarithms $\log _ { 12 } \sqrt { \frac { \mathrm { rs } } { 13 } }$