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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- \frac{3}{2} \cdot ln (\frac{a}{b})

5 lo g_{h} (y) + 4 lo g_{h} (x)

- \frac{1}{3} ln ∣ x + 1 ∣ + \frac{1}{3} ln ∣ x - 2 ∣ + 3

ln (6) + ln (\frac{e ^{(2.43849)}}{3})

ln (7 (- 4)^{2} (2) (3))

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