simplify 4ln(16/21)

Solution

simplify

4 ln (\frac{16}{21})

4 (4 ln (2) - ln (21))

Decimal Notation

- 1.08773 \dots

Solution steps

4 ln (\frac{16}{21})

Apply log rule:

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

ln (\frac{16}{21}) = ln (16) - ln (21)

= 4 (ln (16) - ln (21))

ln (16) = 4 ln (2)

= 4 (4 ln (2) - ln (21))

lo g_{3} (\frac{3}{2}) + lo g_{3} (4.5)

\frac{1}{2} lo g_{10} (x) - lo g_{10} (3 y)

ln (\frac{9310}{3045})

2 lo g_{10} (x) - lo g_{10} (7)

\frac{1}{6} [5 ln (x + 7) - ln (x) - ln (x^{2} - 4)]