Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{2^{x - 3}} = {3^{{x^2} - 5x + 6}}\\
\Leftrightarrow {\log _2}{2^{x - 3}} = {\log _2}{3^{{x^2} - 5x + 6}}\\
\Leftrightarrow \left( {x - 3} \right){\log _2}2 = \left( {{x^2} - 5x + 6} \right){\log _2}3\\
\Leftrightarrow \left( {x - 3} \right).1 = \left( {x - 2} \right)\left( {x - 3} \right){\log _2}3\\
\Leftrightarrow \left( {x - 3} \right)\left[ {1 - \left( {x - 2} \right).{{\log }_2}3} \right] = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 3 = 0\\
1 - \left( {x - 2} \right).{\log _2}3 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x - 2 = \frac{1}{{{{\log }_2}3}}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = 2 + {\log _3}2
\end{array} \right.
\end{array}\)
