化简 2000ln((140000)/(140000-2100(8)))-9.8(8)

解答

化简

2000 ln (\frac{140000}{140000 - 2100 ( 8 )}) - 9.8 (8)

2000 (ln (140000) - ln (123200)) - 78.4

十进制

177.26674 \dots

求解步骤

2000 ln (\frac{140000}{140000 - 2100 ( 8 )}) - 9.8 (8)

使用对数计算法则:

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

ln (\frac{140000}{140000 - 2100 ( 8 )}) = ln (140000) - ln (140000 - 2100 (8))

= 2000 (ln (140000) - ln (140000 - 2100 \cdot 8)) - 8 \cdot 9.8

ln (140000 - 2100 \cdot 8) = ln (123200)

= 2000 (ln (140000) - ln (123200)) - 8 \cdot 9.8

数字相乘:

9.8 \cdot 8 = 78.4

= 2000 (ln (140000) - ln (123200)) - 78.4

s im pl i f y ln (x) - ln (t)

s im pl i f y \frac{5}{14} lo g_{2} (\frac{5}{14}) + \frac{9}{14} lo g_{2} (\frac{9}{14})

s im pl i f y lo g_{10} (0.1) - lo g_{10} (0.2)

s im pl i f y - lo g_{10} (4.7 \cdot 1 0^{- 6})

s im pl i f y - lo g_{10} (7.45 \cdot 1 0^{- 6})