simplify ln(6/16)

Solution

simplify

ln (\frac{6}{16})

ln (6) - 4 ln (2)

Decimal Notation

- 0.98082 \dots

Solution steps

ln (\frac{6}{16})

Apply log rule:

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

ln (\frac{6}{16}) = ln (6) - ln (16)

= ln (6) - ln (16)

ln (16) = 4 ln (2)

= ln (6) - 4 ln (2)

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

- lo g_{10} (\frac{1 0 ^{- 14}}{2 \cdot 1 0 ^{- 9}})

ln (\frac{4.67 \cdot 1 0 ^{22}}{5 \cdot 1 0 ^{22}})

\frac{1}{6} ln ∣ sin (6 x) ∣ - \frac{1}{6} ln ∣ cos (6 x) ∣