simplify 2*ln(1/6)

Solution

simplify

2 \cdot ln (\frac{1}{6})

- 2 ln (6)

Decimal Notation

- 3.58351 \dots

Solution steps

2 ln (\frac{1}{6})

Apply log rule:

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

ln (\frac{1}{6}) = ln (1) - ln (6)

= 2 (ln (1) - ln (6))

Apply log rule:

lo g_{a} (1) = 0

= 2 (- ln (6) + 0)

0 - ln (6) = - ln (6)

= 2 (- ln (6))

Remove parentheses:

(- a) = - a

= - 2 ln (6)

\frac{( ln ( 20 ) + ln ( 25 ) )}{3 ln ( 5 )}

\frac{1}{2} ln (9 x^{2}) + 2 ln (x) - 3 ln (2 x)

- 2 ln ∣ ln (x) ∣ - ln (x)

10 \cdot ln (0.5 \cdot X)

6 lo g_{9} (x) - 3 lo g_{9} (y)