What is 1/9 ln(1/8) ?

The solution to 1/9 ln(1/8) is -1/3 ln(2)

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simplify 1/9 ln(1/8)

simplify

\frac{1}{9} ln (\frac{1}{8})

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

Decimal Notation

- 0.23104 \dots

Solution steps

\frac{1}{9} ln (\frac{1}{8})

Apply log rule:

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

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

= \frac{1}{9} (ln (1) - ln (8))

Apply log rule:

lo g_{a} (1) = 0

= \frac{1}{9} (- ln (8) + 0)

0 - ln (8) = - ln (8)

= \frac{1}{9} (- ln (8))

Remove parentheses:

(- a) = - a

= - \frac{1}{9} ln (8)

Simplify

ln (8) : 3 ln (2)

= - 3 \cdot \frac{1}{9} ln (2)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot 3}{9} ln (2)

\frac{1 \cdot 3}{9} = \frac{1}{3}

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

3 lo g_{10} (a - 1) + lo g_{10} (a + 2)

2 (ln (2) - ln (3))

ln (tan (y) tan (x))

ln (\frac{15.88}{6.67})

- lo g_{10} (5.011 \cdot 1 0^{- 9})