What is ln(((x+1)^2)/((x-1)^4)) ?

The solution to ln(((x+1)^2)/((x-1)^4)) is 2ln(x+1)-4ln(x-1)

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simplify ln(((x+1)^2)/((x-1)^4))

simplify

ln (\frac{( x + 1 ) ^{2}}{( x - 1 ) ^{4}})

2 ln (x + 1) - 4 ln (x - 1)

Solution steps

ln (\frac{( x + 1 ) ^{2}}{( x - 1 ) ^{4}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{( x + 1 ) ^{2}}{( x - 1 ) ^{4}}) = ln ((x + 1)^{2}) - ln ((x - 1)^{4})

= ln ((x + 1)^{2}) - ln ((x - 1)^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x + 1)^{2}) = 2 ln (x + 1)

= 2 ln (x + 1) - ln ((x - 1)^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x - 1)^{4}) = 4 ln (x - 1)

= 2 ln (x + 1) - 4 ln (x - 1)

- lo g_{10} (3.5 \cdot 1 0^{- 11})

4 ln ∣ x ∣ + 4 ln ∣ x + 1 ∣ + C

\frac{84 ln ( \frac{200}{119} )}{ln ( \frac{40}{17} )}

ln (\frac{x ( x + 2 ) ^{2}}{( x - 2 ) ^{3}})

ln (\frac{373}{298})

What is ln(((x+1)^2)/((x-1)^4)) ?
The solution to ln(((x+1)^2)/((x-1)^4)) is 2ln(x+1)-4ln(x-1)