simplify ln(1/12)

Solution

simplify

ln (\frac{1}{12})

- ln (12)

Decimal Notation

- 2.48490 \dots

Solution steps

ln (\frac{1}{12})

Apply log rule:

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

ln (\frac{1}{12}) = ln (1) - ln (12)

= ln (1) - ln (12)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (12)

0 - ln (12) = - ln (12)

= - ln (12)

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

\frac{1}{3} lo g_{2} (3) + \frac{2}{3} lo g_{2} (\frac{3}{2})

lo g_{2} ((r + s) \cdot t)

4 lo g_{10} (x) + 2 lo g_{10} (y)

\frac{1}{3} lo g_{3} (x^{6}) + \frac{1}{6} lo g_{3} (x^{6}) - \frac{1}{9} lo g_{3} (x)