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

question 309

Multiple Choice

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) \(\frac { 1 } { 2 } \log _ { 12 } \mathrm { r } + \frac { 1 } { 2 } \log _ { 12 } \mathrm {~s} - \frac { 1 } { 2 } \log _ { 12 } 13\)

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Definitions:

Conglomerate

A sedimentary rock made up of rounded or semi-rounded fragments within a finer-grained matrix, often indicating a high-energy environment such as a fast-flowing river.

Sandstone

A sedimentary rock consisting of sand or quartz grains cemented together, typically red, yellow, or brown in color.

Quartz

A hard, crystalline mineral composed of silicon dioxide, commonly found in many types of rocks and used in various industrial applications.

Sedimentary Rock

Rock formed from the accumulation of sediment, which can be transported by water, wind, or ice, and often contains fossils.