What is 1/3 ln((3(e^{x^3})^3)/(x^6)) ?

The solution to 1/3 ln((3(e^{x^3})^3)/(x^6)) is 1/3 (ln(3e^{3x^3})-6ln(x))

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simplify 1/3 ln((3(e^{x^3})^3)/(x^6))

simplify

\frac{1}{3} ln \frac{3 ( e ^{x^{3}} ) ^{3}}{x ^{6}}

\frac{1}{3} (ln (3 e^{3 x^{3}}) - 6 ln (x))

Solution steps

\frac{1}{3} ln \frac{3 ( e ^{x^{3}} ) ^{3}}{x ^{6}}

Apply log rule:

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

ln \frac{3 ( e ^{x^{3}} ) ^{3}}{x ^{6}} = ln (3 (e^{x^{3}})^{3}) - ln (x^{6})

= \frac{1}{3} (ln (3 (e^{x^{3}})^{3}) - ln (x^{6}))

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= \frac{1}{3} (ln (3 (e^{x^{3}})^{3}) - 6 ln (x))

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

= \frac{1}{3} (ln (3 e^{3 x^{3}}) - 6 ln (x))

lo g_{10} (\frac{85347 \times 15274}{125386})

lo g_{10} (3) + lo g_{10} (6) - 2 lo g_{10} (4)

\frac{1}{4} ln (2)

3 ln (x) + 5 ln (y) - 4 ln (z)

ln (14 x y)

What is 1/3 ln((3(e^{x^3})^3)/(x^6)) ?
The solution to 1/3 ln((3(e^{x^3})^3)/(x^6)) is 1/3 (ln(3e^{3x^3})-6ln(x))