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}})

lo g_{7} (k^{2} - 49) - lo g_{7} (k - 7)

2 - lo g_{7} (6) - 2 lo g_{7} (x)

lo g_{7} (k^{2} - 49) - lo g_{7} (k) - 7

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

ln (\frac{1}{100})

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))