What is ln((3(\sqrt[4]{3}))/9) ?

The solution to ln((3(\sqrt[4]{3}))/9) is -3/4 ln(3)

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simplify ln((3(\sqrt[4]{3}))/9)

simplify

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

Decimal Notation

- 0.82395 \dots

Solution steps

Apply log rule:

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

Apply log rule:

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

= ln (3) + \frac{1}{4} ln (3) - ln (9)

Add similar elements:

ln (3) + \frac{1}{4} ln (3) = \frac{5}{4} ln (3)

= \frac{5}{4} ln (3) - ln (9)

ln (9) = 2 ln (3)

= \frac{5}{4} ln (3) - 2 ln (3)

Factor out common term

ln (3)

= ln (3) (\frac{5}{4} - 2)

\frac{5}{4} - 2 = - \frac{3}{4}

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

36 \cdot ln (9) - 36 \cdot ln (4)

ln (p) + ln (10000 - p)

ln (\frac{14}{5 \cdot 1 0 ^{31}})

- \frac{6}{8} (\frac{4}{6} lo g_{2} (\frac{4}{6}) + \frac{1}{6} lo g_{2} (\frac{1}{6}))

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

What is ln((3(\sqrt[4]{3}))/9) ?
The solution to ln((3(\sqrt[4]{3}))/9) is -3/4 ln(3)