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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{1}{θ} \cdot e^{- \frac{1}{θ} \cdot x})

ln (\frac{- 4}{1 + I})

12 (ln ∣ (0) + 2 ∣ - ln ∣ (0) + 3 ∣) + C

ln (\frac{1}{\frac{1}{n}})

ln (\frac{388}{363})

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