Expanding logarithmic expressions in exercise, use the properties of logarithms to rewrite the expression as the sum, difference, or multiple of logarithms.
in(x - 1/x + 1)^2

Step-by-step explanation:

We know that , the properties of logarithm are:

P[1]  

P[2]  

P[3]  

The given expression in terms of Natural log :

     [ By using P[3]]

[ By using Property (1)]

Hence, the simplified expression becomes .

We can use two properties to solve:

Quotient Rule:

Power Rule:

Simplify the expression using the power rule:

In(x - 1/x + 1)^2 → 2 ln (x - 1/x + 1)

Simplify using the quotient rule:

2 ln (x - 1/x + 1) → 2[ln(x - 1) - ln(x + 1)]

Therefore, the the simplified logarithm is 2[ln(x - 1) - ln(x + 1)]

Best of Luck!

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