KIẾN THỨC CẦN GHI NHỚ
1. ${a^{f\left( x \right)}} = {a^{g\left( x \right)}}$ $ \Leftrightarrow f\left( x \right) = g\left( x \right).$
2. ${a^{f\left( x \right)}} = b = {a^{{{\log }_a}b}}$ $ \Leftrightarrow f\left( x \right) = {\log _a}b.$
3. ${a^{f\left( x \right)}} = {b^{g\left( x \right)}}$ $ \Leftrightarrow f\left( x \right) = g\left( x \right){\log _a}b.$
4. ${a^{f\left( x \right)}} > {a^{g\left( x \right)}}$ $(1).$
- Nếu $a > 1$ thì $\left( 1 \right) \Leftrightarrow f\left( x \right) > g\left( x \right).$
- Nếu $0 < a < 1$ thì $\left( 1 \right) \Leftrightarrow f\left( x \right) < g\left( x \right).$
Hay $\left( 1 \right) \Leftrightarrow \left\{ \begin{array}{l}
a > 0\\
\left( {a – 1} \right)\left( {f\left( x \right) – g\left( x \right)} \right) > 0
\end{array} \right.$