Đáp án:

\(\begin{array}{l}
10)\quad S = \{-3\}\\
11)\quad S = \left\{\dfrac92\right\}\\
12)\quad S = \{\ln2;\ln3\}\\
13)\quad S = \{1\}\\
14)\quad S = \{-1;1\}\\
15)\quad S = \{-1;0\}\\
16)\quad S = \left\{-\dfrac{\ln3}{\ln2};0\right\}\\
17)\quad S = \{0\}\\
18)\quad S = \{0\}\\
19)\quad S = \{-4;1\}\\
20)\quad S = \{1\}\\
21)\quad S = \{-1\}\\
22)\quad S = \left\{-\dfrac12\right\}\\
23)\quad S = \left\{-\sqrt3;\sqrt3\right\}\\
24)\quad S = \{9\}\\
25)\quad S = \left\{\log_68;3\right\}\\
26)\quad S = \left\{\dfrac{\pi}{2} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}\\
27)\quad S = \left\{-\sqrt2;-1;1;\sqrt2\right\}\\
28)\quad S = \left\{\log_{40}4000\right\}\\
29)\quad S = \{1;3\}\\
30)\quad S = \left\{\dfrac{\ln\dfrac23}{\ln2};1\right\}
\end{array}\)  

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\}\\
12)\quad e^{2x}  -3.e^x - 4 + 12.e^{-x} = 0\\
\Leftrightarrow e^{3x} - 3.e^{2x} - 4.e^x + 12 = 0\\
\Leftrightarrow (e^x +2)(e^x - 2)(e^x -3) = 0\\
\Leftrightarrow \left[\begin{array}{l}e^x = -2\quad (vn)\\e^x = 2\\e^x = 3\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = \ln2\\x = \ln3\end{array}\right.\\
\text{Vậy}\ S = \{\ln2;\ln3\}\\
13)\quad 4.9^x +12^x - 3.16^x =0\\
\Leftrightarrow 4.3^{2x} + 3^x.4^x - 3.4^{2x} = 0\\
\Leftrightarrow 4.\left(\dfrac34\right)^{2x} + \left(\dfrac34\right)^x - 3 =0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac34\right)^x = \dfrac34\\\left(\dfrac34\right)^x = -1\quad (vn)\end{array}\right.\\
\Leftrightarrow x = 1\\
\text{Vậy}\ S = \{1\}\\
14)\quad 6.9^x -13.6^x  + 6.4^x = 0\\
\Leftrightarrow 6.3^{2x} - 13.3^x.2^x + 6.2^{2x} = 0\\
\Leftrightarrow 6.\left(\dfrac32\right)^{2x} - 13.\left(\dfrac32\right)^x + 6 = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac32\right)^x = \dfrac23\\\left(\dfrac32\right)^x = \dfrac32\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = -1\\x = 1\end{array}\right.\\
\text{Vậy}\ S = \{-1;1\}\\
15)\quad 2.2^{2x}- 9. 14^x + 7.7^{2x} = 0\\
\Leftrightarrow 2.\left(\dfrac27\right)^{2x} - 9.\left(\dfrac27\right)^x + 7 = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac27\right)^x = 1\\\left(\dfrac27\right)^x = \dfrac72\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = 0\\x = -1\end{array}\right.\\
\text{Vậy}\ S = \{-1;0\}\\
16)\quad 3^x.2^{x^2} = 1\\
\Leftrightarrow e^{\ln3^x}.e^{\ln2^{x^2}} = 1\\
\Leftrightarrow e^{x\ln3 + x^2\ln2} = 1\\
\Leftrightarrow x\ln3 + x^2\ln2 = 0\\
\Leftrightarrow x(\ln3 + x\ln2) = 0\\
\Leftrightarrow \left[\begin{array}{l}x = 0\\x = -\dfrac{\ln3}{\ln2}\end{array}\right.\\
\text{Vậy}\ S = \left\{-\dfrac{\ln3}{\ln2};0\right\}\\
17)\quad 5.25^x - 3.10^x = 2.4^x\\
\Leftrightarrow 5.5^{2x} - 3.5^x.2^x - 2.2^{2x} = 0\\
\Leftrightarrow 5.\left(\dfrac52\right)^{2x} - 3.\left(\dfrac52\right)^x - 2 =0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac52\right)^x = 1\\\left(\dfrac52\right)^x = -\dfrac25\quad (vn)\end{array}\right.\\
\Leftrightarrow x = 0\\
\text{Vậy}\ S = \{0\}\\
18)\quad 2.4^x + 6^x = 3.9^x\\
\Leftrightarrow 2.2^{2x} + 2^x.3^x - 3.3^{2x} = 0\\
\Leftrightarrow 2.\left(\dfrac23\right)^{2x} + \left(\dfrac23\right)^x - 3 =0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac23\right)^x = 1\\\left(\dfrac23\right)^x = -\dfrac32\quad (vn)\end{array}\right.\\
\Leftrightarrow x = 0\\
\text{Vậy}\ S = \{0\}\\
19)\quad 3^{2x^2 +6x - 9} + 4.15^{x^2 +3x - 5} = 3.5^{2x^2 + 6x - 9}\\
\Leftrightarrow 5.3^{2(x^2 + 3x - 4)} + 4.3^{x^2 + 3x - 4}.5^{x^2 + 3x - 4} - 9.5^{2(x^2 + 3x - 4)} = 0\\
\Leftrightarrow 5.\left(\dfrac35\right)^{2(x^2 + 3x - 4)} + 4.\left(\dfrac35\right)^{x^2 + 3x - 4} - 9 = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac35\right)^{x^2 + 3x - 4} = 1\\\left(\dfrac35\right)^{x^2 + 3x - 4} = -\dfrac95\quad (vn)\end{array}\right.\\
\Leftrightarrow x^2 +3x - 4 =0\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = -4\end{array}\right.\\
\text{Vậy}\ S = \{-4;1\}\\
20)\quad \left(2^{3x} - \dfrac{8}{2^{3x}}\right) - 6.\left(2^x - \dfrac{1}{2^{x-1}}\right) = 1\\
\Leftrightarrow (2^x)^3 - 6\cdot 2^x + 12\cdot \dfrac{2}{2^x} - \left(\dfrac{2}{2^x}\right)^3 = 1\\
\Leftrightarrow (2^x)^3 - 3\cdot (2^x)^2\cdot \dfrac{2}{2^x} + 3\cdot 2^x\cdot \left(\dfrac{2}{2^x}\right)^2 - \left(\dfrac{2}{2^x}\right)^3 = 1\\
\Leftrightarrow \left(2^x - \dfrac{2}{2^x}\right)^3 = 1\\
\Leftrightarrow 2^x - \dfrac{2}{2^x} = 1\\
\Leftrightarrow 2^{2x} - 2^x - 2 =0\\
\Leftrightarrow \left[\begin{array}{l}2^x = -1\quad (vn)\\2^x = 2\end{array}\right.\\
\Leftrightarrow x = 1\\
\text{Vậy}\ S = \{1\}\\
21)\quad (0,4)^x- (2,5)^{x+1} = 1,5\\
\Leftrightarrow \left(\dfrac25\right)^x - \dfrac52\cdot \left(\dfrac52\right)^x = \dfrac32\\
\Leftrightarrow 2.\left(\dfrac25\right)^{2x} - 3.\left(\dfrac25\right)^x - 5 = 0\\
\Leftrightarrow \left[\begin{array}{l}\left(\dfrac25\right)^x = -1\quad (vn)\\\left(\dfrac25\right)^x = \dfrac52\end{array}\right.\\
\Leftrightarrow x = -1\\
\text{Vậy}\ S = \{-1\}\\
22)\quad 3.4^x +\dfrac13.9^{x+2} = 6.4^{x+1} - \dfrac12.9^{x+1}\\
\Leftrightarrow 6.4^x + 54.9^x = 48.4^x - 9.9^x\\
\Leftrightarrow 63.9^x = 42.4^x\\
\Leftrightarrow \left(\dfrac94\right)^x = \dfrac23\\
\Leftrightarrow \left(\dfrac32\right)^{2x} = \left(\dfrac32\right)^{-1}\\
\Leftrightarrow 2x = -1\\
\Leftrightarrow x = -\dfrac12\\
\text{Vậy}\ S = \left\{-\dfrac12\right\}\\
23)\quad 2^{x^2 - 1} - 3^{x^2} = 3^{x^2 - 1} - 2^{x^2+2}\\
\Leftrightarrow 2^{x^2 - 1} - 3.3^{x^2 - 1} = 3^{x^2 - 1} - 8.2^{x^2 - 1}\\
\Leftrightarrow 9.2^{x^2 - 1} = 4.3^{x^2 - 1}\\
\Leftrightarrow \left(\dfrac23\right)^{x^2 - 1} = \dfrac49\\
\Leftrightarrow x^2 - 1 = 2\\
\Leftrightarrow x = \pm \sqrt3\\
\end{array}\) 

\(\begin{array}{l}\text{Vậy}\ S = \left\{-\sqrt3;\sqrt3\right\}\\
24)\quad 2^{\sqrt x + 2} - 2^{\sqrt x + 1} = 12 + 2^{\sqrt x - 1}\quad (ĐK:x\geqslant 0)\\
\Leftrightarrow 8.2^{\sqrt x- 1} - 4.2^{\sqrt x - 1} = 12 + 2^{\sqrt x - 1}\\
\Leftrightarrow 2^{\sqrt x - 1} = 4\\
\Leftrightarrow \sqrt x - 1 = 2\\
\Leftrightarrow \sqrt x = 3\\
\Rightarrow x = 9\quad \text{(nhận)}\\
\text{Vậy}\ S = \{9\}\\
25)\quad 64^{\tfrac1x} - 2^{3 + \tfrac3x} + 12 = 0\qquad (ĐK:x\ne 0)\\
\Leftrightarrow \left(8^{\tfrac1x}\right)^2 - 8.8^{\tfrac1x} + 12 = 0\\
\Leftrightarrow \left[\begin{array}{l}8^{\tfrac1x} = 2\\8^{\tfrac1x} = 6\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}\dfrac1x = \log_82\\\tfrac1x = \log_86\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = \log_28\\x = \log_68\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = 3\\x = \log_68\end{array}\right.\quad \text{(nhận)}\\
\text{Vậy}\ S = \left\{\log_68;3\right\}\\
26)\quad 2^{\sin^2x} +4.2^{\cos^2x}  - 6 =0\\
\Leftrightarrow 2^{\sin^2x} + 4.2^{1-\sin^2x} - 6 =0\\
\Leftrightarrow 2^{2\sin^2x} - 6.2^{\sin^2x} + 8 = 0\\
\Leftrightarrow \left[\begin{array}{l}2^{\sin^2x} = 2\\2^{\sin^2x} = 4\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}\sin^2x = 1\\\sin^2x = 2\quad (vn)\end{array}\right.\\
\Leftrightarrow \dfrac{1 - \cos2x}{2} = 1\\
\Leftrightarrow \cos2x = -1\\
\Leftrightarrow 2x = \pi + k2\pi\\
\Leftrightarrow x = \dfrac{\pi}{2} + k\pi\quad (k\in\Bbb Z)\\
\text{Vậy}\ S = \left\{\dfrac{\pi}{2} + k\pi\ \Bigg|\ k\in\Bbb Z\right\}\\
27)\quad 9^{x^2 - 1} - 36.3^{x^2 - 3} + 3 = 0\\
\Leftrightarrow 81.3^{2(x^2 - 3)} - 36.3^{x^2 - 3} + 3 = 0\\
\Leftrightarrow \left[\begin{array}{l}3^{x^2 - 3} = \dfrac19\\3^{x^2 - 3} = \dfrac13\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}3^{x^2 - 3} = 3^{-2}\\3^{x^2 - 3} = 3^{-1}\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x^2 - 3 = -2\\x^2 - 3 = -1\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x^2 = 1\\x^2 = 2\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = \pm 1\\x = \pm \sqrt2\end{array}\right.\\
\text{Vậy}\ S = \left\{-\sqrt2;-1;1;\sqrt2\right\}\\
28)\quad 5^x.8^{x-1} = 500\\
\Leftrightarrow 5^x.8^x = 4000\\
\Leftrightarrow 40^x = 4000\\
\Leftrightarrow x = \log_{40}4000\\
\text{Vậy}\ S = \left\{\log_{40}4000\right\}\\
29)\quad 8.3^x + 3.2^x = 24 + 6^x\\
\Leftrightarrow (3^x - 3)(2^x - 8) = 0\\
\Leftrightarrow \left[\begin{array}{l}3^x = 3\\2^x = 8\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = 3\end{array}\right.\\
\text{Vậy}\ S = \{1;3\}\\
30)\quad 3^{x-1}.2^{x^2} = 8.4^{x-2}\\
\Leftrightarrow 3^{x-1}.2^{x^2} = 2^{2x -1}\\
\Leftrightarrow 3^{x-1}.2^{x^2 - 2x + 1} = 1\\
\Leftrightarrow e^{\ln3^{x-1}}.e^{\ln2^{x^2 -2x + 1}} = 1\\
\Leftrightarrow e^{(x-1)\ln3 + (x-1)^2\ln2} = 1\\
\Leftrightarrow (x-1)\ln3 + (x-1)^2\ln2 = 0\\
\Leftrightarrow (x-1)[\ln3 + (x-1)\ln2] = 0\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = 1 - \dfrac{\ln3}{\ln2}\end{array}\right.\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = \dfrac{\ln\dfrac23}{\ln2}\end{array}\right.\\
\text{Vậy}\ S = \left\{\dfrac{\ln\dfrac23}{\ln2};1\right\}
\end{array}\)