What is 3ln(x^4e^{x^3}) ?

The solution to 3ln(x^4e^{x^3}) is 12ln(x)+3x^3

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simplify 3ln(x^4e^{x^3})

simplify

3 ln (x^{4} e^{x^{3}})

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

Solution steps

3 ln (x^{4} e^{x^{3}})

Apply log rule:

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

3 ln (x^{4} e^{x^{3}}) = 3 ln (x^{4}) + 3 ln (e^{x^{3}})

= 3 ln (x^{4}) + 3 ln (e^{x^{3}})

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= 3 \cdot 4 ln (x) + 3 ln (e^{x^{3}})

Apply log rule:

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

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

= 3 \cdot 4 ln (x) + 3 x^{3} ln (e)

3 \cdot 4 ln (x) = 12 ln (x)

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

= 12 ln (x) + 3 x^{3}

3 ln (\frac{cos ( x ) + 1}{9 - x ^{2}})

ln \frac{n r t}{\frac{\frac{3 p}{n r t}}{p}}

2 ln (a) + 2 ln (b) - ln (a)

88 + 10 \cdot lo g_{10} (\frac{2}{4 \cdot 3.14 \cdot 1 0 ^{2}})