5. Use the properties of logarithms to condense: 3 In x - 2 In (x + 1)

Step-by-step explanation:

The given expression is

3In x - 2In (x + 1)

We would apply the rule of logarithm which is expressed as

ylog x = logx^y

Therefore,

3In x - 2In (x + 1) = lnx^3 - ln (x + 1) ^2

We would apply another rule of logarithm which is expressed as

loga - logb = loga/b

Therefore

lnx^3 - ln (x + 1) ^2 = ln x^3 / (x + 1) ^2