simplify ln(49/99)

Solution

simplify

ln (\frac{49}{99})

2 ln (7) - ln (99)

Decimal Notation

- 0.70329 \dots

Solution steps

ln (\frac{49}{99})

Apply log rule:

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

ln (\frac{49}{99}) = ln (49) - ln (99)

= ln (49) - ln (99)

ln (49) = 2 ln (7)

= 2 ln (7) - ln (99)

3 + 10 lo g_{10} (5) - 40 lo g_{10} (2)

- lo g_{10} (4.6 \cdot 1 0^{- 10})

lo g_{e} (6) - lo g_{e} (2)

\frac{300}{2 \cdot π \cdot 1000} \cdot ln (\frac{4 + 2 \cdot 100 0 ^{2}}{25})

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ x - 4 ∣ + C