What is 1/2 ln(4/5) ?

The solution to 1/2 ln(4/5) is ln(2)-1/2 ln(5)

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simplify 1/2 ln(4/5)

simplify

\frac{1}{2} ln (\frac{4}{5})

ln (2) - \frac{1}{2} ln (5)

Decimal Notation

- 0.11157 \dots

Solution steps

\frac{1}{2} ln (\frac{4}{5})

Apply log rule:

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

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

= \frac{1}{2} (ln (4) - ln (5))

ln (4) = 2 ln (2)

= \frac{1}{2} (2 ln (2) - ln (5))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{2}, b = 2 ln (2), c = ln (5)

= \frac{1}{2} \cdot 2 ln (2) - \frac{1}{2} ln (5)

= 2 \cdot \frac{1}{2} ln (2) - \frac{1}{2} ln (5)

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

= ln (2) - \frac{1}{2} ln (5)

ln (2 x) + ln (e)

2 ln (x) + ln (c)

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