Logarithms

Under Construction: Consider this content a preview of the real thing which is coming soon (hopefully).

graph LR
    classDef currentPage stroke:#333,stroke-width:4px

	ALG(["fas:fa-trophy Algorithmis fas:fa-trophy "])

	ASY_ANA(["fas:fa-check Asymptotic Analysis#160;"])
    click ASY_ANA "./math-asymptotic-analysis"

    

	MAT_NOT(["fas:fa-check Mathematical Notation#160;"])
    click MAT_NOT "./math-notation"

    

	POL(["fas:fa-check Polynomials #160;"])
    click POL "./math-polynomials"

    

	MAT_FUN(["fas:fa-check Math Functions#160;"])
    click MAT_FUN "./math-functions"

    

	LOG(["fas:fa-check Logarithms#160;"])
    click LOG "./math-logarithms"

    
      class LOG currentPage
    

	COM(["fas:fa-check Combinatorics#160;"])
    click COM "./math-combinatorics"

    

	SET_NOT(["fas:fa-check Set Notation#160;"])
    click SET_NOT "./math-set-notation"

    

	GRA(["fas:fa-check Graphing#160;"])
    click GRA "./math-graphing"

    

	BW(["fas:fa-check Bitwise Logic#160;"])
    click BW "./math-bitwise"

    

	ASY_ANA-->ALG
	BW-->ALG
    COM & GRA & SET_NOT-->ASY_ANA
    MAT_NOT--> SET_NOT
    POL & LOG--> MAT_FUN
    MAT_FUN--> GRA

There is much variation in way people use logarithms.

To a mathematician, $\log{x}$ means $\log_{10}{x}$, and the natural log is always $\ln{x}$. To a physicist, $\log{x}$ is the natural logarithm. To an engineer (not computer), $\log{x}=log_{10}{x}$. To a computer engineer, $\log{x}=\log_2{x}$.

  • $\log_x{n}$ (logarithm base $x$)
  • $\lg{n} = \log_2{n}$ (binary logarithm)
  • $\ln{n} = \log_e{n}$ (natural logarithm)
  • $\lg^k{n} = (\lg{n})^k$ (exponentiation)
  • $\lg{\lg{n}} = \lg{(\lg{n})}$ (composition)
  • $\lg^*{n}$ (iterated)