Question

Type each expression as a sum or difference of logs. Expand and simplify the logarithm as much as possible. When typing your answer do not put any spaces between the characters and use parentheses () with your logarithm. For example, log(x) has parentheses on each side of the x. log(\frac{x}{z}{w})

Answer 1

We can use the following logarithm rules:

`\begin{gathered} \log _a(xy)=\log _a(x)+\log _a(y)\Rightarrow\text{ Product rule} \\ \log _a((x)/(y))=_{}\log _a(x)-\log _a(y)\Rightarrow\text{ Quotient rule} \end{gathered}`

Then, we have:

`\begin{gathered} \text{ Apply the product rule} \\ \log ((x)/(z)w)=\log ((x)/(z))+\log (w) \\ \text{ Apply the quotient rule} \\ \log ((x)/(z)w)=\log (x)-\log (z)+\log (w) \end{gathered}`

Therefore, the given expression expanded as a sum or difference of logs is:

`\log (x)-\log (z)+\log (w)`