What is ln(1/2)*ln(1/2) ?

The solution to ln(1/2)*ln(1/2) is ln^2(2)

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simplify ln(1/2)*ln(1/2)

simplify

ln (\frac{1}{2}) \cdot ln (\frac{1}{2})

ln^{2} (2)

Decimal Notation

0.48045 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= (ln (1) - ln (2)) (ln (1) - ln (2))

Simplify

(ln (1) - ln (2)) (ln (1) - ln (2)) : (ln (1) - ln (2))^{2}

Apply log rule:

lo g_{a} (1) = 0

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

0 - ln (2) = - ln (2)

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

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

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

= ln^{2} (2)

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