simplify ln(3/81)

Solution

simplify

ln (\frac{3}{81})

- 3 ln (3)

Decimal Notation

- 3.29583 \dots

Solution steps

ln (\frac{3}{81})

Apply log rule:

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

ln (\frac{3}{81}) = ln (3) - ln (81)

= ln (3) - ln (81)

ln (81) = 4 ln (3)

= ln (3) - 4 ln (3)

Add similar elements:

ln (3) - 4 ln (3) = - 3 ln (3)

= - 3 ln (3)

3.15 + lo g_{10} (\frac{1.875}{0.625})

\frac{1}{2} (ln (5) - ln (4))

- 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣

20 lo g_{10} (4 π) - 20 lo g_{10} (300000)

- ln ∣ x + 2 ∣ + 2 ln ∣ x - 3 ∣ + C