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Diogo Gomes · Answer 1 · 2023-09-23T07:28:03+0000

Solution

- The question would like us to determine the difference expression that corresponds to the following logarithm

$\log_a((M)/(N))$

- In order to solve this question, we should apply the Law of Logarithm which states that:

$\log A-\log B=\log((A)/(B))$

- Applying this law, we have:

$\begin{gathered} \text{ Let A from the formula be M and Let B from the formula be N from the question} \\ Note\text{ that }a\text{ in the question is represented by 10 from the formula. The base 10 in logarithm is usually not } \\ \text{ indicated} \\ \\ \log_a((M)/(N))=\log_aM-\log_aN \end{gathered}$

Final Answer

The answer to the question is

$\operatorname{\log}_(a)((M)/(N))=\operatorname{\log}_(a)M-\operatorname{\log}_(a)N$

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