simplify ln(e/8)

Solution

simplify

ln (\frac{e}{8})

1 - 3 ln (2)

Decimal Notation

- 1.07944 \dots

Solution steps

ln (\frac{e}{8})

Apply log rule:

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

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

= ln (e) - ln (8)

Apply log rule:

lo g_{a} (a) = 1

= 1 - ln (8)

ln (8) = 3 ln (2)

= 1 - 3 ln (2)

lo g_{10} (a b^{2} c)

ln (x e^{(\frac{y}{z})})

- \frac{ln ( \frac{9}{2} ) - ln ( \frac{25}{2} )}{4}

- lo g_{10} (1.4 \cdot 1 0^{- 6})

\frac{20}{100} \cdot ln (\frac{20}{100})