simplify ln(21/8)

Solution

simplify

ln (\frac{21}{8})

ln (21) - 3 ln (2)

Decimal Notation

0.96508 \dots

Solution steps

ln (\frac{21}{8})

Apply log rule:

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

ln (\frac{21}{8}) = ln (21) - ln (8)

= ln (21) - ln (8)

ln (8) = 3 ln (2)

= ln (21) - 3 ln (2)

ln (\frac{x ^{4} y ^{5}}{z ^{3}})

lo g_{7} (10) - lo g_{7} (3) - 4 lo g_{7} (x)

lo g_{10} (4.5 x 1 0^{- 4})

lo g_{2} (9 x) - 4 lo g_{2} (4) - 1

ln ∣ x ∣ + \frac{1}{6 ( \frac{y}{x} ) ^{2}} - ln \frac{y}{x}