Answered

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

Sagot :

We will use the following two properties of the logarithmic function

[tex]\begin{gathered} \ln (\frac{M}{N})=\ln M-\ln N \\ \text{and} \\ \ln (M^a)=a\ln M \end{gathered}[/tex]

Therefore, given

[tex]\ln (\frac{x^3}{e^2})[/tex]

Simplify as shown below

[tex]\begin{gathered} \ln (\frac{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 (\frac{x^3}{e^2})=3\ln (x)-2 \end{gathered}[/tex]

The answer is 3ln(x)-2

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