simplify 2ln(201/8)

Solution

simplify

2 ln (\frac{201}{8})

2 (ln (201) - 3 ln (2))

Decimal Notation

6.44772 \dots

Solution steps

2 ln (\frac{201}{8})

Apply log rule:

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

ln (\frac{201}{8}) = ln (201) - ln (8)

= 2 (ln (201) - ln (8))

ln (8) = 3 ln (2)

= 2 (ln (201) - 3 ln (2))

- 1 - 5 \cdot ln (\frac{1.5}{4})

ln (\frac{1}{999})

ln (2 x + 1) - ln (x + 1)

- lo g_{10} (1.4 (1 0^{- 5}))

ln (x (x + 2) (x + 9))