simplify ln(2/4)

Solution

simplify

ln (\frac{2}{4})

- ln (2)

Decimal Notation

- 0.69314 \dots

Solution steps

ln (\frac{2}{4})

Apply log rule:

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

ln (\frac{2}{4}) = ln (2) - ln (4)

= ln (2) - ln (4)

ln (4) = 2 ln (2)

= ln (2) - 2 ln (2)

Add similar elements:

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

= - ln (2)

4 lo g_{7} (x) - 3 lo g_{7} (y)

- lo g_{10} (5 \cdot 1 0^{- 8})

ln ((x (4 y - 1)^{\frac{1}{3}})^{\frac{2}{5}})

ln (4 e^{2 x})

lo g_{5} (\frac{x}{25})