What is ln^2(1/3)-(ln(1/3))^2 ?

The solution to ln^2(1/3)-(ln(1/3))^2 is -2ln^2(3)

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simplify ln^2(1/3)-(ln(1/3))^2

simplify

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

- 2 ln^{2} (3)

Decimal Notation

- 2.41389 \dots

Solution steps

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

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} (\frac{1}{3})

ln^{2} (1) = 0

= 0 - ln^{2} (3) - ln^{2} (\frac{1}{3})

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

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

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

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

Add similar elements:

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

= - 2 ln^{2} (3)

- 2 ln (1 - x) + ln (x + 2)

ln (sin (x)) + ln (x + y)

13 ln (\frac{208}{3}) + 7 ln (80 - 0.75 \cdot \frac{208}{3})

ln (\frac{41}{10}) - \frac{1}{4}

\frac{1}{4} ln (x + 2) - \frac{1}{4} ln (x - 2)

What is ln^2(1/3)-(ln(1/3))^2 ?
The solution to ln^2(1/3)-(ln(1/3))^2 is -2ln^2(3)