simplify 3+3ln(2/3)

Solution

simplify

3 + 3 ln (\frac{2}{3})

3 + 3 (ln (2) - ln (3))

Decimal Notation

1.78360 \dots

Solution steps

3 + 3 ln (\frac{2}{3})

Apply log rule:

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

ln (\frac{2}{3}) = ln (2) - ln (3)

= 3 + 3 (ln (2) - ln (3))

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

- \frac{ln ( 42 )}{ln ( 7 ) - ln ( 6 )}

ln (u) - \frac{1}{2} ln 1 + u^{2} + \frac{1}{2 ( 1 + u ^{2} )} + C

(- \frac{1}{3}) ln (\frac{2}{3})

ln (\frac{x ^{8} x ^{2} + 2}{( x + 2 ) ^{3}})