can't understand answer for partial fraction

[kluda06]

I high lighted what I am confused about. Can someone explain to me how it becomes (x+3)^2 as well as how ln x combines with ln (x+3)^2

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[stapel]

The text in the image is too small for me to read. Could you type things out, or post larger images? Thank you!

 

[Deleted member 4993]

View attachment 3281

I high lighted what I am confused about. Can someone explain to me how it becomes (x+3)^2 as well as how ln x combines with ln (x+3)^2

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Those come from the following rules of logarithms:

b * ln(a) = ln(a^b)

and

ln(p) + ln(q) = ln(p*q)

and

ln(m) - ln(n) =\(\displaystyle \displaystyle ln\left (\frac{m}{n}\right )\)