Question

Use properties of logarithms to condense the logarithmic expression below. Coefficient is 1. 5 In x-4 In y

Answer 1

To answer this question we will use the following properties of the natural logarithm:

`\begin{gathered} m\ln b=\ln b^m, \\ \ln a-\ln b=\ln(a)/(b). \end{gathered}`

Using the first property we can rewrite the given expression as follows:

`ln(x^5)-ln(y^4).`

Using the second property we get:

`\ln(x^5)/(y^4).`

Answer:

`\ln(x^5)/(y^4).`