simplify 2ln(4/3)

Solution

simplify

2 ln (\frac{4}{3})

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

Decimal Notation

0.57536 \dots

Solution steps

2 ln (\frac{4}{3})

Apply log rule:

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

ln (\frac{4}{3}) = ln (4) - ln (3)

= 2 (ln (4) - ln (3))

ln (4) = 2 ln (2)

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

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

ln (\frac{2}{x ^{2}})

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

lo g_{e} (\frac{2117}{1000})

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