${\log _a}1 = 0{\text{ (0 < a}} \ne {\text{1)}}$
${\log _a}a = 1{\text{ (0 < a}} \ne {\text{1)}}$
${\log _a}{a^\alpha } = \alpha {\text{ (0 < a}} \ne {\text{1)}}$
${\log _{{a^\alpha }}}a = \frac{1}{\alpha }{\text{ (0 < a}} \ne {\text{1)}}$
${\log _a}{b^\alpha } = \alpha .{\log _a}{\text{b (a, b > 0, a}} \ne {\text{1)}}$
${\log _{{a^\beta }}}b = \frac{1}{\beta }.{\log _a}{\text{b}}$
${\log _{{a^\beta }}}{b^\alpha } = \frac{\alpha }{\beta }.{\log _a}{\text{b}}$
${\log _a}b + {\log _a}c = {\log _a}(b.c)$
${\log _a}b - {\log _a}c = {\log _a}\left( {\frac{b}{c}} \right)$
${\log _a}b = \frac{1}{{{{\log }_b}a}}$
${\log _a}b = \frac{{{{\log }_c}b}}{{{{\log }_c}a}}$
${\log _a}b = \alpha $ thì $b = {a^\alpha }$
${\left( {{{\log }_a}b} \right)^\alpha } = {\log ^\alpha }_ab$
$\ln a = {\log _e}a$
${a^{{{\log }_a}\alpha }} = \alpha $
$\lg a = \log a = {\log _{10}}a$
${\log _a}b = {\log _a}c$ thì b = c
${\log _a}b < {\log _a}c$ thì b < c ${\text{(a}} > 1)$
${\log _a}b < {\log _a}c$ thì $b > c{\text{ }}(0 < a < 1)$
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