# 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)