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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

Respuesta :

JeanaShupp

Answer:  [tex]2[\ln(x-1)-\ln(x+1)][/tex]

Step-by-step explanation:

We know that , the properties of logarithm are:

P[1]  [tex]\log (ab)= \log a+\log b[/tex]

P[2]  [tex]\log(\dfrac{a}{b})=\log a-\log b[/tex]

P[3]  [tex]\log a^n= n\log a[/tex]

The given expression in terms of Natural log : [tex] \ln (\dfrac{x-1}{x+1})^{2}[/tex]

[tex]=2\ln ((\dfrac{x-1}{x+1})[/tex]      [ By using P[3]]

[tex]=2[\ln(x-1)-\ln(x+1)][/tex] [ By using Property (1)]

Hence, the simplified expression becomes [tex]2[\ln(x-1)-\ln(x+1)][/tex] .

Wolfyy

We can use two properties to solve:

Quotient Rule: [tex]\text{ln}\frac{x}{y} = \text{ln}(x)-\text{ln}(y)[/tex]

Power Rule: [tex]\text{ln}(x)^p = p~\text{ln}(x)[/tex]

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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