\(4^x-10\times2^x+16=0\)
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\(4^x-10.2^x+16=0\)
\(\Leftrightarrow\left(2^x\right)^2-10.2^x+16=0\)
Đặt 2x = t
\(\Rightarrow t^2-10t+16=0\)
\(\Leftrightarrow t^2-2t-8t+16=0\)
\(\Leftrightarrow t\left(t-2\right)-8\left(t-2\right)=0\)
\(\Leftrightarrow\left(t-2\right)\left(t-8\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}t=2\\t=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2^x=2\\2^x=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
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\(4^x-10\times2^x+16=0\)
\(\Leftrightarrow2^{2x}-2\times5\times2^x+16=0\)
\(\Leftrightarrow\left[\left(2^x\right)^2-2\times2^x\times5+25\right]-9=0\)
\(\Leftrightarrow\left(2^x-5\right)^2-3^2=0\)
\(\Leftrightarrow\left(2^x-5-3\right)\left(2^x-5+3\right)=0\)
\(\Leftrightarrow\left(2^x-8\right)\left(2^x-2\right)=0\)
\(\Leftrightarrow2^x-8=0\) hoặc \(2^x-2=0\)
\(\cdot2^x-8=0\Leftrightarrow2^x=8\Leftrightarrow x=3\)
\(\cdot2^x-2=0\Leftrightarrow2^x=2\Leftrightarrow x=1\)
Vậy \(S=\left\{3;1\right\}\)
\(4^x-10\cdot2^x+16=0\)
\(=\left(2^x\right)^2-10\cdot2^x+16=0\)
Đặt \(t=2^x\). Ta có:
\(t^2-10t+16=0\)
\(\Rightarrow t^2-2\cdot t\cdot5+25-9=0\)
\(\Rightarrow\left(t-5\right)^2-3^2=0\)
\(\Rightarrow\left(t-8\right)\left(t-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}t=8\\t=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)
Vậy S = {1,3}
![](https://rs.olm.vn/images/avt/0.png?1311)
a ) \(\left(3\times x-15\right)^7=0.\)
\(3\times x-15=0\)
\(3\times x=15\)
\(x=5\)
b ) \(10-\left\{\left[\left(x\div3+17\right)\div10+3\times2^4\right]\div10\right\}=5\)
\(10-\left\{\left[\left(x\div3+17\right)\div10+3\times16\right]\div10\right\}=5\)
\(10-\left\{\left[\left(x\div3+17\right)\div10+48\right]\div10\right\}=5\)
\(\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)
\(\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)
\(\left(x\div3+17\right)\div10+48=50\)
\(\left(x\div3+17\right)\div10=2\)
\(x\div3+17=20\)
\(x\div3=3\)
\(x=9\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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a) (x - 1/2) x 2 = 9/16
=> x - 1/2 = 9/16 : 2
=> x - 1/2 = 9/16 x 1/2
=> x - 1/2 =9/32
=> x = 9/32 + 1/2
=> x = 25/32
b) |x + 1/2| = 3/4
=> x + 1/2 = 3/4 hoặc x + 1/2 =-3/4
=>x = 3/4 - 1/2 hoặc x = -3/4 -1/2
=>x = 1/4 hoặc x = -5/4
Vậy .........
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\(E=\dfrac{11.3^{29}-3^{2^{15}}}{2.3^{14}.2.3^{14}}\)
\(=\dfrac{11.3-3^{30}}{2^2}=\dfrac{33-3^{30}}{4}\)