simplify ln^2(1/3)

Solution

simplify

ln^{2} (\frac{1}{3})

- ln^{2} (3)

Decimal Notation

- 1.20694 \dots

Solution steps

ln^{2} (\frac{1}{3})

Apply log rule:

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

ln^{2} (\frac{1}{3}) = ln^{2} (1) - ln^{2} (3)

= ln^{2} (1) - ln^{2} (3)

ln^{2} (1) = 0

= 0 - ln^{2} (3)

0 - ln^{2} (3) = - ln^{2} (3)

= - ln^{2} (3)

4 (\frac{1}{9} ln ∣ x ∣ - \frac{1}{18} ln x^{2} + 3 + \frac{1}{6 ( x ^{2} + 3 )})

- lo g_{10} (2.6 \cdot 1 0^{- 7})

ln (d) - ln (a \cdot b) + ln (c)

6 lo g_{7} (7 x + 1) + \frac{1}{4} lo g_{7} (x + 4)

- lo g_{10} (4.55 \cdot 1 0^{- 8})