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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (x) - 4 lo g_{10} (y) + 5 lo g_{10} (z)

ln (\frac{r}{6 s})

lo g_{10} (\frac{5 a}{3 b})

lo g_{10} (2 x^{- 3})

lo g_{2} (2 x + 1) - lo g_{2} (x - 3)

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