Problem

Write the following expression in expanded form.
\[
\ln [x(x-1)]
\]
\[
\ln [x(x-1)]=
\]

Answer

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Answer

Final Answer: \(\boxed{\ln [x(x-1)]= \ln x + \ln (x-1)}\)

Steps

Step 1 :Write the following expression in expanded form: \(\ln [x(x-1)]\)

Step 2 :The natural logarithm, ln, has a property that allows the logarithm of a product to be written as the sum of the logarithms of the individual factors.

Step 3 :In this case, the expression inside the logarithm, x(x-1), is a product of x and (x-1). Therefore, we can use the property of logarithms to write this as the sum of the logarithms of x and (x-1).

Step 4 :Final Answer: \(\boxed{\ln [x(x-1)]= \ln x + \ln (x-1)}\)

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