simplify ln(1/(x!))

Solution

simplify

ln (\frac{1}{x !})

- ln (x!)

Solution steps

ln (\frac{1}{x !})

Apply log rule:

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

ln (\frac{1}{x !}) = ln (1) - ln (x!)

= ln (1) - ln (x!)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (x!)

0 - ln (x!) = - ln (x!)

= - ln (x!)

lo g_{b} (\frac{x ^{2} \cdot y}{z ^{6}})

\frac{1}{2} lo g_{4} (25) + lo g_{4} (2)

- \frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

ln (\frac{e ^{8 x} + 1}{e ^{- 3 x} + 1})

- \frac{6}{9} lo g_{2} (\frac{6}{9}) - \frac{3}{9} lo g_{2} (\frac{3}{9})