化简-ln(0.01sqrt(1-0.46^2))

解答

化简

- ln (0.01 1 - 0.4 6^{2})

- ln (0.01) - \frac{ln ( 0.7884 )}{2}

十进制

4.72404 \dots

求解步骤

- ln (0.01 1 - 0.4 6^{2})

使用对数计算法则:

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

ln (0.01 1 - 0.4 6^{2}) = ln (0.01) + ln (1 - 0.4 6^{2})

= - (ln (0.01) + ln (1 - 0.4 6^{2}))

ln (1 - 0.4 6^{2}) = \frac{ln ( 0.7884 )}{2}

= - (\frac{ln ( 0.7884 )}{2} + ln (0.01))

打开括号

= - (ln (0.01)) - (\frac{ln ( 0.7884 )}{2})

使用加减运算法则

+ (- a) = - a

= - ln (0.01) - \frac{ln ( 0.7884 )}{2}

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