What is expand ln(((x^4(x+1)^3))/((x-1)^4)) ?

The solution to expand ln(((x^4(x+1)^3))/((x-1)^4)) is 4ln(x)+3ln(x+1)-4ln(x-1)

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expand ln(((x^4(x+1)^3))/((x-1)^4))

expand

ln \frac{( x ^{4} ( x + 1 ) ^{3} )}{( x - 1 ) ^{4}}

4 ln (x) + 3 ln (x + 1) - 4 ln (x - 1)

Solution steps

ln \frac{( x ^{4} ( x + 1 ) ^{3} )}{( x - 1 ) ^{4}}

Apply log rule:

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

ln \frac{( x ^{4} ( x + 1 ) ^{3} )}{( x - 1 ) ^{4}} = ln ((x^{4} (x + 1)^{3})) - ln ((x - 1)^{4})

= ln (x^{4} (x + 1)^{3}) - 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)

= ln (x^{4} (x + 1)^{3}) - 4 ln (x - 1)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (x^{4} (x + 1)^{3}) = ln (x^{4}) + ln ((x + 1)^{3})

= ln (x^{4}) + ln ((x + 1)^{3}) - 4 ln (x - 1)

Apply log rule:

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

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

= 4 ln (x) + ln ((x + 1)^{3}) - 4 ln (x - 1)

Apply log rule:

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

ln ((x + 1)^{3}) = 3 ln (x + 1)

= 4 ln (x) + 3 ln (x + 1) - 4 ln (x - 1)

8 lo g_{b} (x) + 9 lo g_{b} (y) - 4 lo g_{b} (z)

\frac{23}{2} (2 \cdot ln (\frac{a ^{3}}{b}) + 22 \cdot ln (\frac{1}{b}))

ln (\frac{2}{25}) - ln (\frac{2}{4})

5 ln ∣ x - 1 ∣ - ln ∣ x ∣

\frac{1}{3} ln ∣ tan (x) + sec (x) ∣

What is expand ln(((x^4(x+1)^3))/((x-1)^4)) ?
The solution to expand ln(((x^4(x+1)^3))/((x-1)^4)) is 4ln(x)+3ln(x+1)-4ln(x-1)