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:

$\begin{gathered} m\ln b=\ln b^m, \\ \ln a-\ln b=\ln\frac{a}{b}. \end{gathered}$

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

$\ln{x^5}-\ln{y^4}.$

Using the second property we get:

$\ln\frac{x^5}{y^4}.$

Answer:

$\ln\frac{x^5}{y^4}.$