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

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

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simplify 1/2 ln(1/4)

simplify

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

- ln (2)

Decimal Notation

- 0.69314 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= \frac{1}{2} (- ln (4) + 0)

0 - ln (4) = - ln (4)

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

Remove parentheses:

(- a) = - a

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

Simplify

ln (4) : 2 ln (2)

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

Multiply fractions:

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

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

Cancel the common factor:

2

= - ln (2) \cdot 1

Multiply:

ln (2) \cdot 1 = ln (2)

= - ln (2)

20 \cdot lo g_{10} (4 \cdot 3.1415 \cdot x \cdot (8.16))

lo g_{2} (3 a)

ln (\frac{1}{b - a})

3 lo g_{10} (2) - lo g_{10} (5)

ln (\frac{- 4.1 + 8.05}{31.8})