simplify ln(15/400)

Solution

simplify

ln (\frac{15}{400})

ln (15) - 2 ln (20)

Decimal Notation

- 3.28341 \dots

Solution steps

ln (\frac{15}{400})

Apply log rule:

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

ln (\frac{15}{400}) = ln (15) - ln (400)

= ln (15) - ln (400)

ln (400) = 2 ln (20)

= ln (15) - 2 ln (20)

ln (\frac{17}{5})

- ln (- b (ln (a)))

\frac{3}{5} ln (x) - 7 ln (y)

- 5 + ln (\frac{29}{4})

2 (3 ln (4) - ln ((4 + 1) (4 - 1)))