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i am fengdy.

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多项式

  1. (a+b)n=Cn0an+...+Cnkan−kbk+...+Cnnbn(a+b)^n = C_n^0a^n + ... + C_n^ka^{n-k}b^k + ... + C_n^nb^n

指数

  1. a−n=1a(a≠0)a^{-n} = \frac{1}{a} (a\neq0)
  2. amn=amna^{\frac{m}{n}} = \sqrt[n]{a^m}

对数

  1. alog⁡aN=Na^{\log_a^N} = N
  2. log⁡abn=nlog⁡ab\log_a^{b^n} = n\log_a^b
  3. log⁡aa=1\log_a^a = 1
  4. log⁡a1=0\log_a^1 = 0
  5. log⁡aMN=log⁡aM+log⁡aN\log_a^{MN} = \log_a^M + \log_a^N
  6. log⁡aMN=log⁡aM−log⁡aN\log_a^{\frac{M}{N}} = \log_a^M - \log_a^N
  7. log⁡ab=1log⁡ba\log_a^b = \frac{1}{\log_b^a}
  8. lg⁡a=log⁡10a\lg a = \log_{10}^a
  9. ln⁡a=log⁡ea\ln a = \log_e^a