What is ln((x^2(x+1)^3)/(\sqrt[4]{x-1)}) ?

The solution to ln((x^2(x+1)^3)/(\sqrt[4]{x-1)}) is 2ln(x)+3ln(x+1)-ln(\sqrt[4]{x-1})

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simplify ln((x^2(x+1)^3)/(\sqrt[4]{x-1)})

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

ln (x^{2} (x + 1)^{3}) = ln (x^{2}) + ln ((x + 1)^{3})

Apply log rule:

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

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

Apply log rule:

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

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

ln (\frac{47}{50})

\frac{π}{8} ln (3)

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

- 0.7 \cdot lo g_{2} (0.7) - 0.3 lo g_{2} (0.3)

ln (\frac{2.3}{1.5})

What is ln((x^2(x+1)^3)/(\sqrt[4]{x-1)}) ?
The solution to ln((x^2(x+1)^3)/(\sqrt[4]{x-1)}) is 2ln(x)+3ln(x+1)-ln(\sqrt[4]{x-1})