Solution
- The question would like us to determine the difference expression that corresponds to the following logarithm
[tex]\log_a(\frac{M}{N})[/tex]
- In order to solve this question, we should apply the Law of Logarithm which states that:
[tex]\log A-\log B=\log(\frac{A}{B})[/tex]
- Applying this law, we have:
[tex]\begin{gathered} \text{ Let A from the formula be M and Let B from the formula be N from the question} \\ Note\text{ that }a\text{ in the question is represented by 10 from the formula. The base 10 in logarithm is usually not } \\ \text{ indicated} \\ \\ \log_a(\frac{M}{N})=\log_aM-\log_aN \end{gathered}[/tex]
Final Answer
The answer to the question is
[tex]\operatorname{\log}_{a}(\frac{M}{N})=\operatorname{\log}_{a}M-\operatorname{\log}_{a}N[/tex]
