What is ln((e^{-x^3})(3x^3)) ?

The solution to ln((e^{-x^3})(3x^3)) is -x^3+ln(3)+3ln(x)

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simplify ln((e^{-x^3})(3x^3))

simplify

ln ((e^{- x^{3}}) (3 x^{3}))

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

Solution steps

ln ((e^{- x^{3}}) (3 x^{3}))

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((e^{- x^{3}}) (3 x^{3})) = ln (e^{- x^{3}}) + ln (3 x^{3})

= ln (e^{- x^{3}}) + ln (3 x^{3})

Apply log rule:

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

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

= - x^{3} ln (e) + ln (3 x^{3})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

= - ln (e) x^{3} + ln (3) + ln (x^{3})

Apply log rule:

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

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

= - x^{3} ln (e) + ln (3) + 3 ln (x)

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

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

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

lo g_{5} (7 \cdot 3)

7 lo g_{3} (y) - \frac{1}{4} lo g_{3} (z) + 2 lo g_{3} (x)

ln ∣ x + 2 ∣ - \frac{1}{2} ln y^{2} - 1

lo g_{10} (\frac{x ^{3} y}{z})

What is ln((e^{-x^3})(3x^3)) ?
The solution to ln((e^{-x^3})(3x^3)) is -x^3+ln(3)+3ln(x)