Question

What’s equivalent to ln(x^3/e^2)Ln X-93ln x-23ln x+63ln x-6

Answer 1

We will use the following two properties of the logarithmic function

`\begin{gathered} \ln ((M)/(N))=\ln M-\ln N \\ \text{and} \\ \ln (M^a)=a\ln M \end{gathered}`

Therefore, given

`\ln ((x^3)/(e^2))`

Simplify as shown below

`\begin{gathered} \ln ((x^3)/(e^2))=\ln (x^3)-\ln (e^2) \\ =3\ln (x)-2\ln (e);\ln (e)=1 \\ =3\ln (x)-2\cdot1 \\ =3\ln (x)-2 \\ \Rightarrow\ln ((x^3)/(e^2))=3\ln (x)-2 \end{gathered}`

The answer is 3ln(x)-2