simplify ln(27/150)

Solution

simplify

ln (\frac{27}{150})

3 ln (3) - ln (150)

Decimal Notation

- 1.71479 \dots

Solution steps

ln (\frac{27}{150})

Apply log rule:

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

ln (\frac{27}{150}) = ln (27) - ln (150)

= ln (27) - ln (150)

ln (27) = 3 ln (3)

= 3 ln (3) - ln (150)

lo g_{10} (a) - 6 lo g_{10} (c)

- lo g_{3} (75 \cdot 1 0^{- 3})

ln (\frac{28.5}{43.5})

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

12 ln (x + 0.125) + 13 ln (4 x + 1)