化简 (ln(2.98)-ln(3))/((2.98)-3)

解答

化简

\frac{ln ( 2.98 ) - ln ( 3 )}{( 2.98 ) - 3}

- \frac{ln ( 0.99333 \dots )}{0.02}

十进制

0.33444 \dots

求解步骤

\frac{ln ( 2.98 ) - ln ( 3 )}{( 2.98 ) - 3}

使用对数计算法则:

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

ln (2.98) - ln (3) = ln (\frac{2.98}{3})

= \frac{ln ( \frac{2.98}{3} )}{2.98 - 3}

数字相除:

\frac{2.98}{3} = 0.99333 \dots

= \frac{ln ( 0.99333 \dots )}{2.98 - 3}

数字相减:

2.98 - 3 = - 0.02

= \frac{ln ( 0.99333 \dots )}{- 0.02}

使用分式法则:

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

= - \frac{ln ( 0.99333 \dots )}{0.02}

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