What is 1/3 ln(11/8) ?

The solution to 1/3 ln(11/8) is 1/3 ln(11)-ln(2)

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simplify 1/3 ln(11/8)

simplify

\frac{1}{3} ln (\frac{11}{8})

\frac{1}{3} ln (11) - ln (2)

Solution steps

\frac{1}{3} ln (\frac{11}{8})

Apply log rule:

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

ln (\frac{11}{8}) = ln (11) - ln (8)

= \frac{1}{3} (ln (11) - ln (8))

ln (8) = 3 ln (2)

= \frac{1}{3} (ln (11) - 3 ln (2))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{3}, b = ln (11), c = 3 ln (2)

= \frac{1}{3} ln (11) - \frac{1}{3} \cdot 3 ln (2)

= \frac{1}{3} ln (11) - 3 \cdot \frac{1}{3} ln (2)

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

= \frac{1}{3} ln (11) - ln (2)

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