simplify ln(32/67)

Solution

simplify

ln (\frac{32}{67})

5 ln (2) - ln (67)

Decimal Notation

- 0.73895 \dots

Solution steps

ln (\frac{32}{67})

Apply log rule:

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

ln (\frac{32}{67}) = ln (32) - ln (67)

= ln (32) - ln (67)

ln (32) = 5 ln (2)

= 5 ln (2) - ln (67)

- 2 ln (2 e)

92.45 + 20 lo g_{10} (18.2 \cdot 85)

ln (10000) - ln (5000)

\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4

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