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

The solution to simplify-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))

Apply rule

- (- 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)

ln (\frac{273}{264})

ln (\frac{a + a ^{2} + x ^{2}}{x})

- ln (3) - ln (x) - ln (5 x)

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

\frac{1}{2} ln ∣ 8.7 + 4 ∣ - \frac{1}{2} ln ∣ 8.7 + 6 ∣ + C