simplify ln(5/1000)

Solution

simplify

ln (\frac{5}{1000})

ln (5) - 3 ln (10)

Decimal Notation

- 5.29831 \dots

Solution steps

ln (\frac{5}{1000})

Apply log rule:

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

ln (\frac{5}{1000}) = ln (5) - ln (1000)

= ln (5) - ln (1000)

ln (1000) = 3 ln (10)

= ln (5) - 3 ln (10)

lo g_{b} (\frac{x ^{3} \cdot y}{z ^{3}})

5 lo g_{4} (x) + 9 lo g_{4} (y)

ln ∣ 7 ∣ - ln ∣ 4 ∣

ln (\frac{x ^{1.5}}{1.5})

3 ln (x) + ln (e x)