Solving logarithmic and exponential equations

Revise the laws of logarithms in order to solve logarithmic and exponential equations

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To work with logarithmic equations, you need to remember the laws of logarithms:

${\log _a}a = 1$ (since ${a^1} = a$ ) so ${\log _7}7 = 1$
${\log _a}1 = 0$ (since ${a^0} = 1$ ) so ${\log _{20}}1 = 0$
${\log _a}p + {\log _a}q = {\log _a}pq$ so ${\log _3}2 + {\log _3}5 = {\log _3}10$
${\log _a}p - {\log _a}q = {\log _a}\frac{p}{q}$ so ${\log _6}54 - {\log _6}9 = {\log _6}\frac{{54}}{9} = {\log _6}6 = 1$
${\log _a}{p^n} = n{\log _a}p$ so ${\log _2}{5^3} = 3{\log _2}5$