simplify ln(1/2)*2

Solution

simplify

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

- 2 ln (2)

Solution steps

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

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

Apply log rule:

lo g_{a} (1) = 0

= 2 (- ln (2) + 0)

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

= 2 (- ln (2))

Remove parentheses:

(- a) = - a

= - ln (2) \cdot 2

ln (5) + ln (20)

ln (\frac{( 1 - i )}{( 1 + i )})

ln (x) - ln (2 x - 1)

\frac{ln ( 7 ) - 5 ln ( 5 )}{ln ( 5 )}

- \frac{1}{2} ln (20)