Příklad 1

(a) $\begin{cases} 4^{x+y}=128\\5^{3x-2y-3}=1\end{cases}$	(b) $\begin{cases} 2^{2x}+3^y=13\\2\cdot4^x-3^y=-1\end{cases}$
(c) $\begin{cases} 8^{2x+1}=32\cdot2^{4y-1}\\5\cdot5^{x-y}=\sqrt{25^{2y+1}}\end{cases}$	(d) $\begin{cases} 2^{\frac{x+y}3}+2^{\frac{x+y}6}=6\\ x^2+y^2=6xy\end{cases}$
(e) $\begin{cases} x^{y^2-4y+4}=1\\ x+y=6\end{cases}$	(f) $\begin{cases} 3^{x+1} + 4^{y+2} = 54\\ 3^{x+2} + 4^{y+1} = 30\end{cases}$
(g $\begin{cases}2^{\frac{x-y}{2}}+2^{\frac{y-x}{2}}=\frac{5}{2}\\4^{x-2y}-7\cdot2^{x-2y}=8\end{cases}$	(h) $\begin{cases} \sqrt[x]{x+y}=3\\ 2^{x-2}\cdot(x+y)=9\end{cases}$
(i) $\begin{cases} \sqrt[4]{2^x}\cdot\sqrt{2^y}=8\sqrt{2}\\ \sqrt{2^{x-2}}\cdot\sqrt[3]{2^{y+1}}=16\sqrt[3]{2}\end{cases}$	(j) $\begin{cases} 5^{x+1}+3^{y+1}=26\\9(5^{2x}+3^{2y})=226\end{cases}$

Řešení	Ukázat
(a) $[x;y]=[2;\frac32]$ (b) $[x;y]=[1;2]$ (c) $[x;y]=[\frac3{14};\frac1{14}]$ (d) $[x;y]=[\frac{6\pm3\sqrt2}2;\frac{6\mp3\sqrt2}2]$ (e) $[x;y]\in\{[1;5];[4;2]\}$ (f) $[x;y]=[\frac{\ln2}{\ln3};\frac{\ln3}{2\ln2}]$ (g) $[x;y]\in\{[1;-1];[-7;-5]\}$ (h) $[x;y]=[2;7]$ (i) $[x;y]=[8;3]$ (j) $[x;y]\in\{[1;-1];[\log_5(\frac{45}{17});\log_3(\frac{217}{51})]$

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