化简 3/(sqrt(41))ln(2e)

解答

化简

\frac{3}{41} ln (2 e)

\frac{41 ( 3 ln ( 2 ) + 3 )}{41}

十进制

0.79327 \dots

求解步骤

\frac{3}{41} ln (2 e)

使用对数计算法则:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

\frac{3}{41} ln (2 e) = \frac{3}{41} ln (2) + \frac{3}{41} ln (e)

= \frac{3}{41} ln (2) + \frac{3}{41} ln (e)

\frac{3}{41} ln (e) = \frac{3}{41}

= \frac{3}{41} ln (2) + \frac{3}{41}

乘

\frac{3}{41} ln (2) : \frac{3 ln ( 2 )}{41}

= \frac{3 ln ( 2 )}{41} + \frac{3}{41}

因为分母相等，所以合并分式:

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

= \frac{3 ln ( 2 ) + 3}{41}

\frac{3 ln ( 2 ) + 3}{41}

有理化:

\frac{41 ( 3 ln ( 2 ) + 3 )}{41}

= \frac{41 ( 3 ln ( 2 ) + 3 )}{41}

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