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simplificar-ln((sqrt(2))/2)*(sqrt(2))/2

Solução

simplificar

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

\frac{2 ln ( 2 )}{4}

Decimal

0.24506 \dots

Passos da solução

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

Aplicar as propriedades dos logaritmos:

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

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

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

Multiplicar frações:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

2 = 2^{\frac{1}{2}}

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

Aplicar as propriedades dos expoentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

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

Subtrair:

1 - \frac{1}{2} = \frac{1}{2}

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

Aplicar as propriedades dos radicais:

a^{\frac{1}{n}} = n a

2^{\frac{1}{2}} = 2

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

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

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

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

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

Aplicar as propriedades das frações:

\frac{- a}{b} = - \frac{a}{b}

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

Aplicar a regra

- (- a) = a

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

Multiplicar

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

= \frac{\frac{l n ( 2 )}{2}}{2}

Aplicar as propriedades das frações:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

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

Racionalizar

\frac{ln ( 2 )}{2 2} : \frac{2 ln ( 2 )}{4}

= \frac{2 ln ( 2 )}{4}

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