化简 22-ln((1.3810^{-23})/(6.62610^{-34)})

解答

化简

22 - ln (\frac{1.38 \cdot 1 0 ^{- 23}}{6.626 \cdot 1 0 ^{- 34}})

22 - ln (\frac{1.38}{1 0 ^{23}}) + ln (\frac{6.626}{1 0 ^{34}})

十进制

- 1.75951 \dots

求解步骤

22 - ln (\frac{1.38 \cdot 1 0 ^{- 23}}{6.626 \cdot 1 0 ^{- 34}})

使用对数计算法则:

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

ln (\frac{1.38 \cdot 1 0 ^{- 23}}{6.626 \cdot 1 0 ^{- 34}}) = ln (1.38 \cdot 1 0^{- 23}) - ln (6.626 \cdot 1 0^{- 34})

= 22 - (ln (1 0^{- 23} \cdot 1.38) - ln (1 0^{- 34} \cdot 6.626))

- (ln (1.38 \cdot 1 0^{- 23}) - ln (6.626 \cdot 1 0^{- 34})) = - (ln (\frac{1.38}{1 0 ^{23}}) - ln (\frac{6.626}{1 0 ^{34}}))

= 22 - (ln (\frac{1.38}{1 0 ^{23}}) - ln (\frac{6.626}{1 0 ^{34}}))

- (ln (\frac{1.38}{1 0 ^{23}}) - ln (\frac{6.626}{1 0 ^{34}})) : - ln (\frac{1.38}{1 0 ^{23}}) + ln (\frac{6.626}{1 0 ^{34}})

= 22 - ln (\frac{1.38}{1 0 ^{23}}) + ln (\frac{6.626}{1 0 ^{34}})

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