Using logarithm properties, the expression written as a single term is:
[tex]\ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
Researching the problem on a search engine, the expression is given by:
3[2ln(x - 1) - ln(x)] + ln(x + 1).
Applying the distributive property, we have that:
6ln(x - 1) - 3ln(x) + ln(x + 1).
Applying the exponential property of logarithms, we have that the expression is:
[tex]\ln{(x - 1)^6} - \ln{(x)^3} + \ln{(x + 1)}[/tex]
The adding terms can be placed inside multiplying, the subtracting dividing, hence:
[tex]\ln{(x - 1)^6} - \ln{(x)^3} + \ln{(x + 1)} = \ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
Hence the expression written as a single term is:
[tex]\ln{\left(\frac{(x - 1)^6(x+1)}{x^3}\right)}[/tex]
More can be learned about logarithm properties at https://brainly.com/question/25710806
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