simplify 50ln(3/8)

Solution

simplify

50 ln (\frac{3}{8})

50 (ln (3) - 3 ln (2))

Decimal Notation

- 49.04146 \dots

Solution steps

50 ln (\frac{3}{8})

Apply log rule:

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

ln (\frac{3}{8}) = ln (3) - ln (8)

= 50 (ln (3) - ln (8))

ln (8) = 3 ln (2)

= 50 (ln (3) - 3 ln (2))

lo g_{10} (\frac{x}{z ^{5} y ^{3}})

lo g_{10} (\frac{z ^{3} y}{x ^{4}})

\frac{1}{2} lo g_{2} (6) - 2 lo g_{2} (3)

lo g_{4} (\frac{64 a}{b ^{4}})

lo g_{10} (45) + lo g_{10} (\frac{1}{9})