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受欢迎的代数 >

化简-ln((sqrt(2))/2)*(sqrt(2))/2

解答

化简

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

解答

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

+1

十进制

0.24506 \dots

求解步骤

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

使用对数计算法则:

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))

分式相乘:

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

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

使用根式运算法则:

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

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

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

使用指数法则:

\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}}}

数字相减:

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

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

使用根式运算法则:

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}

使用分式法则:

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

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

使用法则

- (- a) = a

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

乘

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

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

使用分式法则:

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

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

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

有理化:

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

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

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