What is ln(x^3+1)-2ln(x-1) ?

The solution to ln(x^3+1)-2ln(x-1) is ln((x^3+1)/((x-1)^2))

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simplify ln(x^3+1)-2ln(x-1)

simplify

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

ln (\frac{x ^{3} + 1}{( x - 1 ) ^{2}})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

f (x) = lo g_{5} (\frac{x ^{2}}{x ^{3}})

8 lo g_{9} (x) + 16 lo g_{9} (y)

\frac{1039}{2} lo g_{2} (1039)

ln (50) - ln (10)

ln (\frac{300}{187})

What is ln(x^3+1)-2ln(x-1) ?
The solution to ln(x^3+1)-2ln(x-1) is ln((x^3+1)/((x-1)^2))