Concept

# List of logarithmic identities

Summary
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes. Trivial identities :{| cellpadding=3 | \log_b(1) = 0 || because || b^0 = 1 |- | \log_b(b) = 1 || because || b^1 = b |} Explanations By definition, we know that: :\color{black} \log \color{blue}_b \color{black} (\color{green}y\color{black}) = \color{red}x\color{black} \iff \color{blue}b\color{black} \color{red}^x\color{black} = \color{green}y\color{black}, where \color{blue}b\color{black} \neq 0 or \color{blue}b\color{black}\neq 1 . Setting \color{red}x\color{black} = 0, we can see that: \color{blue}b\color{black} \color{red}^x\color{black} = \color{green}y\color{black} \iff \color{blue}b\color{black} \color{red}^{(0)}\color{black} = \color{green}y\color{black} \iff \color{blue}1
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