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

The solution to ln^2(1/3)+(ln(1/3))^2 is 0

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

simplify

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

0

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

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

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

Add similar elements:

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

= 0

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