\(\begin{array}{l}
28)\quad 125^x + 50^x = 2^{2x+1}\\
\Leftrightarrow 5^{3x} + 5^{2x}.2^x - 2.2^{2x} = 0\\
\Leftrightarrow \left(\dfrac52\right)^{3x} + \left(\dfrac52\right)^{2x} -2 =0\\
\Leftrightarrow \left[\left(\dfrac52\right)^x -1\right]\left[\left(\dfrac52\right)^{2x} + 2\left(\dfrac52\right)^{x} + 2\right] = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac52\right)^x = 1\\\left(\dfrac52\right)^{2x} + 2\left(\dfrac52\right)^{x} + 2 = 0\quad (vn)\end{array}\right.\\
\Leftrightarrow x = 0\\
\text{Vậy}\ S = \{0\}\\
29)\quad 25^x + 15^x = 2.9^x \\
\Leftrightarrow 5^{2x} + 5^x.3^x - 2.3^{2x} = 0\\
\Leftrightarrow \left(\dfrac53\right)^{2x} + \left(\dfrac53\right)^x - 2 = 0\\
\Leftrightarrow \left[\left(\dfrac53\right)^x-1\right]\left[\left(\dfrac53\right)^x + 2\right] = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac53\right)^x = 1\\\left(\dfrac53\right)^x = -2\quad (vn)\end{array}\right.\\
\Leftrightarrow x = 0\\
\text{Vậy}\ S = \{0\}\\
30)\quad 8.3^{\sqrt x + \sqrt[4]{x}} + 9^{1 + \sqrt[4]{x}} = 9^{\sqrt x}\quad (ĐK:x\geqslant 0)\\
\Leftrightarrow 8.3^{\sqrt x}.3^{\sqrt[4]{x}} + 9.3^{2\sqrt[4]{x}} - 3^{2\sqrt x} = 0\\
\Leftrightarrow \left(3^{\sqrt x} + 3^{\sqrt[4]{x}}\right)\left(9.3^{\sqrt[4]{x}} - 3^{\sqrt x}\right) = 0\\
\Leftrightarrow \left[\begin{array}{l}3^{\sqrt x} + 3^{\sqrt[4]{x}} = 0\quad (vn)\\9.3^{\sqrt[4]{x}} - 3^{\sqrt x} = 0\end{array}\right.\\
\Leftrightarrow 9.3^{\sqrt[4]{x}} = 3^{\sqrt x}\\
\Leftrightarrow 2 + \sqrt[4]{x} = \sqrt x\\
\Leftrightarrow \sqrt x - \sqrt[4]{x} - 2 = 0\\
\leftrightarrow \left(\sqrt[4]{x} + 1\right)\left(\sqrt[4]{x} - 2\right) = 0\\
\Leftrightarrow \left[\begin{array}{l}\sqrt[4]{x} + 1 = 0\quad (vn)\\\sqrt[4]{x} = 2\end{array}\right.\\
\Leftrightarrow x = 16\\
\text{Vậy}\ S = \{16\}
\end{array}\)