What is (-1/3)ln(1/3) ?

The solution to (-1/3)ln(1/3) is 1/3 ln(3)

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simplify (-1/3)ln(1/3)

simplify

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

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

Decimal Notation

0.36620 \dots

Solution steps

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

Apply log rule:

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

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

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

Remove parentheses:

(- a) = - a

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

Apply log rule:

lo g_{a} (1) = 0

= - \frac{1}{3} (- ln (3) + 0)

0 - ln (3) = - ln (3)

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

Apply rule

- (- a) = a

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

2 ln ∣ 4 ∣ + \frac{3}{4} + 3 ln ∣ 5 ∣

ln (1 + 15 - 1) - ln (15)

ln (\frac{108}{162}) \cdot \frac{1}{- 0.01667}

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

ln (\frac{( \frac{0.296}{0.303} )}{9.9})