What is ln((\sqrt[4]{3})/(27)) ?

The solution to ln((\sqrt[4]{3})/(27)) is -11/4 ln(3)

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simplify ln((\sqrt[4]{3})/(27))

simplify

- \frac{11}{4} ln (3)

Decimal Notation

- 3.02118 \dots

Solution steps

Apply log rule:

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

= \frac{1}{4} ln (3) - ln (27)

ln (27) = 3 ln (3)

= \frac{1}{4} ln (3) - 3 ln (3)

Factor out common term

ln (3)

= ln (3) (\frac{1}{4} - 3)

\frac{1}{4} - 3 = - \frac{11}{4}

= - \frac{11}{4} ln (3)

ln (x) + ln ((\frac{y}{x})^{4})

\frac{2}{3} ln (\frac{3 a}{2 s})

ln (2) + ln (- 2)

lo g_{10} ((3 x - 2)^{2})

lo g_{\frac{1}{4}} (\frac{1}{160})

What is ln((\sqrt[4]{3})/(27)) ?
The solution to ln((\sqrt[4]{3})/(27)) is -11/4 ln(3)