What is log_{e}((\sqrt[3]{e^7x})/(x^3)) ?

The solution to log_{e}((\sqrt[3]{e^7x})/(x^3)) is ln(e^2\sqrt[3]{e}\sqrt[3]{x})-3ln(x)

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simplify log_{e}((\sqrt[3]{e^7x})/(x^3))

simplify

Solution steps

Apply log rule:

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

Apply log rule:

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

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

3 lo g_{e} (x) = 3 ln (x)

20 e^{9} + ln (12) + 50 + ln (9)

4 lo g_{10} (x) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

3 ln (\frac{a}{2}) + 2 ln (2 b)

\frac{1}{2} ln (\frac{3}{4})

4 lo g_{2} (x) + lo g_{2} (3) - 2 lo g_{2} (x^{2})

What is log_{e}((\sqrt[3]{e^7x})/(x^3)) ?
The solution to log_{e}((\sqrt[3]{e^7x})/(x^3)) is ln(e^2\sqrt[3]{e}\sqrt[3]{x})-3ln(x)