Đáp án:
\(\begin{array}{l}
10)\quad S = \{-3\}\\
11)\quad S = \left\{\dfrac92\right\}
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
10)\quad 3^{x+4} + 3.5^{x+3} = 5^{x+4} + 3^{x+3}\\
\Leftrightarrow 3.3^{x+3} + 3.5^{x+3} = 5.5^{x+3} + 3^{x+3}\\
\Leftrightarrow 2.3^{x+3} = 2.5^{x+3}\\
\Leftrightarrow \left(\dfrac{3}{5}\right)^{x+3} = 1\\
\Leftrightarrow x+3 = 0\\
\Leftrightarrow x = -3\\
\text{Vậy}\ S = \{-3\}\\
11)\quad 2^{2x-1} + 2^{2x-2} + 2^{2x-3} = 448\\
\Leftrightarrow 4.2^{2x-3} + 2.2^{2x-3} + 2^{2x-3} = 448\\
\Leftrightarrow 7.2^{2x-3} = 448\\
\Leftrightarrow 2^{2x-3} = 64\\
\Leftrightarrow 2x - 3 = 6\\
\Leftrightarrow 2x = 9\\
\Leftrightarrow x = \dfrac92\\
\text{Vậy}\ S = \left\{\dfrac92\right\}
\end{array}\)
