化简 (ln(2.99)-ln(3))/((2.99)-3)

解答

化简

\frac{ln ( 2.99 ) - ln ( 3 )}{( 2.99 ) - 3}

- \frac{ln ( 0.99666 \dots )}{0.01}

十进制

0.33389 \dots

求解步骤

\frac{ln ( 2.99 ) - ln ( 3 )}{( 2.99 ) - 3}

使用对数计算法则:

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

ln (2.99) - ln (3) = ln (\frac{2.99}{3})

= \frac{ln ( \frac{2.99}{3} )}{2.99 - 3}

数字相除:

\frac{2.99}{3} = 0.99666 \dots

= \frac{ln ( 0.99666 \dots )}{2.99 - 3}

数字相减:

2.99 - 3 = - 0.01

= \frac{ln ( 0.99666 \dots )}{- 0.01}

使用分式法则:

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

= - \frac{ln ( 0.99666 \dots )}{0.01}

s im pl i f y - lo g_{10} (4.17 \cdot 1 0^{- 4})

s im pl i f y ln (\frac{x ^{2} - 1}{x - 3})

s im pl i f y 8 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

s im pl i f y - 2.48 ln (\frac{0.67}{1.33})

s im pl i f y ln (\frac{u - a}{u + a})