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Basic properties of logarithms


The logarithm of a given number b is the exponent to which another fixed number, the base a, must be raised, to produce that number b [tex](a>0, \ a\neq 1, \ b>0)[/tex].$$\displaystyle \log_ab=c, \ a^c=b$$
Logarithmic identities
Logarithms of a powers: [tex]\displaystyle \alpha \log _ax=\log _a x^{\alpha}[/tex],  [tex]\frac{1}{\alpha}\log _ax=\log _{a^{\alpha}}x[/tex],  [tex]\displaystyle a^{\log_ax}=x[/tex]
Change of base property: [tex]\displaystyle \log_ax=\frac{\log_bx}{\log_ba}[/tex]
Logarithms of a product and quotient: $\log_ax+\log_ay=\log_axy$,  $\log_ax-\log_ay=\log_a\frac{x}{y}$

Last time edited 2019-01-19

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