\(\begin{array}{l}
1)\\
a)\quad 3^{9-2x} = 27\\
\Leftrightarrow 3^{9-2x} = 3^3\\
\Leftrightarrow 9 - 2x = 3\\
\Leftrightarrow 2x = 6\\
\Leftrightarrow x = 3\\
\text{Vậy}\ S = \{3\}\\
b)\quad 8^{x^2 + x } = 64\\
\Leftrightarrow 8^{x^2 + x} = 8^2\\
\Leftrightarrow x^2 + x = 2\\
\Leftrightarrow x^2 + x - 2 =0\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = -2\end{array}\right.\\
\text{Vậy}\ S = \{-2;1\}\\
c)\quad 25^{x-2} = \left(\dfrac15\right)^x\\
\Leftrightarrow 5^{2x - 4} = 5^{-x}\\
\Leftrightarrow 2x - 4 = -x\\
\Leftrightarrow 3x = 4\\
\Leftrightarrow x = \dfrac43\\
\text{Vậy}\ S = \left\{\dfrac43\right\}\\
d)\quad 16^{x^2 - 4x + 1} = 1\\
\Leftrightarrow x^2 - 4x + 1 =0\\
\Leftrightarrow x = 2\pm \sqrt3\\
\text{Vậy}\ S = \{2 \pm \sqrt3\}\\
2)\\
a)\quad 3^{x-4} >9\\
\Leftrightarrow 3^{x-4} > 3^2\\
\Leftrightarrow x - 4 > 2\\
\Leftrightarrow x > 6\\
\text{Vậy}\ S = (6;+\infty)\\
b)\quad 25^{x-3} > \dfrac15\\
\Leftrightarrow 5^{2x-6} > 5^{-1}\\
\Leftrightarrow 2x - 6 > - 1\\
\Leftrightarrow 2x > 5\\
\Leftrightarrow x > \dfrac52\\
\text{Vậy}\ S = \left(\dfrac52;+\infty\right)\\
3)\\
a)\quad \log_4(3-6x) = 2\qquad \left(ĐK: x < \dfrac12\right)\\
\Leftrightarrow 3-6x = 4^2\\
\Leftrightarrow 6x = -13\\
\Leftrightarrow x = -\dfrac{13}{6}\quad (nhận)\\
\text{Vậy}\ S = \left\{-\dfrac{13}{6}\right\}\\
b)\quad \log_{\sqrt2}(x^2 +6x) = 2\qquad (ĐK: x >0\ \lor\ x < -4)\\
\Leftrightarrow x^2 + 6x = \left(\sqrt2\right)^2\\
\Leftrightarrow x^2 + 6x - 2 =0\\
\Leftrightarrow x = -3 \pm \sqrt{11}\quad (nhận)\\
\text{Vậy}\ S = \{-3 \pm \sqrt{11}\}\\
4)\\
a)\quad A = \log_49 + \log_\sqrt227 - \log_\tfrac123\\
\to A = \log_{2^2}3^2 + \log_{2^{\tfrac12}}3^3 - \log_{2^{-1}}3\\
\to A = \log_23 + 6\log_23 + \log_23\\
\to A = 8\log_23\\
b)\quad B = \log_427.\log_98\\
\to B = \log_{2^2}3^3.\log_3^2.2^3\\
\to B = \dfrac32\log_23\cdot\dfrac32\log_32\\
\to B = \dfrac94\\
5)\\
\quad \log_\tfrac14x + \log_8x =- 6\qquad (ĐK: x >0)\\
\Leftrightarrow \log_{2^{-2}}x + \log_{2^3}x = -6\\
\Leftrightarrow -\dfrac12\log_2x + \dfrac13\log_2x = -6\\
\Leftrightarrow -\dfrac16\log_2x = -6\\
\Leftrightarrow \log_2x = 36\\
\Leftrightarrow x = 2^{36}\quad (nhận)\\
\text{Vậy}\ S = \left\{2^{36}\right\}
\end{array}\)
