What is ln((\sqrt[4]{2})/8) ?

The solution to ln((\sqrt[4]{2})/8) is -11/4 ln(2)

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simplify ln((\sqrt[4]{2})/8)

simplify

- \frac{11}{4} ln (2)

Decimal Notation

- 1.90615 \dots

Solution steps

Apply log rule:

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

= \frac{1}{4} ln (2) - ln (8)

ln (8) = 3 ln (2)

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

Factor out common term

ln (2)

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

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

= - \frac{11}{4} ln (2)

lo g_{10} (y x^{3})

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

lo g_{3} (x) - lo g_{3} (x^{7})

- \frac{1}{20} ln (\frac{1}{2})

lo g_{3} (11) - lo g_{3} (4)

What is ln((\sqrt[4]{2})/8) ?
The solution to ln((\sqrt[4]{2})/8) is -11/4 ln(2)