simplify ln(8/12)

Solution

simplify

ln (\frac{8}{12})

3 ln (2) - ln (12)

Decimal Notation

- 0.40546 \dots

Solution steps

ln (\frac{8}{12})

Apply log rule:

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

ln (\frac{8}{12}) = ln (8) - ln (12)

= ln (8) - ln (12)

ln (8) = 3 ln (2)

= 3 ln (2) - ln (12)

ln (p e^{- c p})

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1))

ln (10 x e^{\frac{- x}{50}})

lo g_{10} (\frac{3 x ^{2} - 15 x}{x ^{2} + 4 x})

ln (\frac{12 x ^{5}}{y})