simplify 2ln(1/5)

Solution

simplify

2 ln (\frac{1}{5})

- 2 ln (5)

Solution steps

2 ln (\frac{1}{5})

Apply log rule:

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

ln (\frac{1}{5}) = ln (1) - ln (5)

= 2 (ln (1) - ln (5))

Apply log rule:

lo g_{a} (1) = 0

= 2 (- ln (5) + 0)

0 - ln (5) = - ln (5)

= 2 (- ln (5))

Remove parentheses:

(- a) = - a

= - 2 ln (5)

ln (a) - 6 ln (b) + 4 ln (c)

ln (2 x) + ln (4 y)

ln (2 π \frac{l}{g})

2 lo g_{10} (x + 3) - lo g_{10} (x - 2)

12 ln (x) + 5 ln (y) - 11 ln (z)