simplify 4*ln(1/2)

Solution

simplify

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

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

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

Apply log rule:

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

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

= 4 (ln (1) - ln (2))

Apply log rule:

lo g_{a} (1) = 0

= 4 (- ln (2) + 0)

0 - ln (2) = - ln (2)

= 4 (- ln (2))

Remove parentheses:

(- a) = - a

= - 4 ln (2)

\frac{1}{2} ln (tan (\frac{x}{2}))

ln (\frac{- a}{2 b - a}) - ln (- 1)

- 8267 ln (\frac{0.07}{100})

- lo g_{10} (9.1 \cdot 1 0^{- 5})