What is 1/2 ln(3/4) ?

The solution to 1/2 ln(3/4) is 1/2 ln(3)-ln(2)

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simplify 1/2 ln(3/4)

simplify

\frac{1}{2} ln (\frac{3}{4})

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

Decimal Notation

- 0.14384 \dots

Solution steps

\frac{1}{2} ln (\frac{3}{4})

Apply log rule:

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

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

= \frac{1}{2} (ln (3) - ln (4))

ln (4) = 2 ln (2)

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

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

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

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

4 lo g_{2} (x) + lo g_{2} (3) - 2 lo g_{2} (x^{2})

lo g_{3} (x^{5} y^{3})

ln (\frac{134.8}{15})

- ln (x y^{2})

\frac{1}{4} lo g_{10} (2)