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a) (32)2x-1 = 3-1 => 32(2x-1) = 3-1 => 2(2x -1) = -1 => 4x - 2 = -1 => 4x = 1 => x = 1/4. vậy,,,
b) 3.8x - 2. (23)x = 64
=> 3.8x - 2.8x = 64
=> 8x = 82 => x = 2
Vậy...
\(a,3.8^x-2.2^{3x}-16=0\)
\(\Leftrightarrow3.\left(2^3\right)^x-2.2^{3x}=16\)
\(\Leftrightarrow3.2^{3x}-2^{3x}=16\)
\(\Leftrightarrow2^{3x}\left(3-1\right)=16\)
\(\Leftrightarrow2^{3x+1}=2^4\)
\(\Leftrightarrow3x+1=4\)
\(\Leftrightarrow3x=3\)
\(\Leftrightarrow x=1\)
Vậy .....
5.23x+1+2.23x+2 - 16 = 0
=> 5.23x.2+2.23x.22 =16
=> 23x ( 10 + 8) = 16
=> 23x = 16:18 = 8/9
=> x khong co gia tri
h) \(\left(x-1\right)^2=25\)
Mà:\(5^2=\left(-5\right)^2=25\)
TH1:\(x-1=5\)
\(x=5+1\)
\(x=6\)
TH2:\(x-1=-5\)
\(x=-5+1\)
\(x=-4\)
Vậy:\(x=6\)hoặc \(x=-4\)
i)\(\left(x+\frac{1}{2}\right)^2=\frac{4}{25}\)
Mà:\(\left(\frac{2}{5}\right)^2=\left(\frac{-2}{5}\right)^2=\frac{4}{25}\)
TH1:\(x+\frac{1}{2}=\frac{2}{5}\) TH2:\(x+\frac{1}{2}=\frac{-2}{5}\)
\(x=\frac{2}{5}-\frac{1}{2}\) \(x=\frac{-2}{5}-\frac{1}{2}\)
\(x=\frac{-1}{10}\) \(x=\frac{-9}{10}\)
Vậy:\(x=\frac{-1}{10}\)hoặc\(x=\frac{-9}{10}\)
b) \(\left(x+\frac{1}{2}\right)^2=\frac{1}{16}\)
\(\Rightarrow\left(x+\frac{1}{2}\right)^2=\left(\pm\frac{1}{4}\right)^2\)
\(\Rightarrow x+\frac{1}{2}=\pm\frac{1}{4}.\)
\(\Rightarrow\left[{}\begin{matrix}x+\frac{1}{2}=\frac{1}{4}\\x+\frac{1}{2}=-\frac{1}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{4}-\frac{1}{2}\\x=\left(-\frac{1}{4}\right)-\frac{1}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-\frac{1}{4}\\x=-\frac{3}{4}\end{matrix}\right.\)
Vậy \(x\in\left\{-\frac{1}{4};-\frac{3}{4}\right\}.\)
c) \(\left(3x+2\right)^3=-27\)
\(\Rightarrow\left(3x+2\right)^3=\left(-3\right)^3\)
\(\Rightarrow3x+2=-3\)
\(\Rightarrow3x=\left(-3\right)-2\)
\(\Rightarrow3x=-5\)
\(\Rightarrow x=\left(-5\right):3\)
\(\Rightarrow x=-\frac{5}{3}\)
Vậy \(x=-\frac{5}{3}.\)
Chúc bạn học tốt!
\(3.8^x-2.2^{3x}-16=0\)
Đề như thế này ạ
\(3.8^x-2.2^{3x}-16=0\)
\(\Leftrightarrow3.\left(2^3\right)^x-2.2^{3x}=16\)
\(\Leftrightarrow3.2^{3x}-2^{3x}=16\)
\(\Leftrightarrow2^{3x}\left(3-1\right)=16\)
\(\Leftrightarrow2^{3x}.2=16\)
\(\Leftrightarrow2^{3x+1}=2^4\)
\(\Leftrightarrow3x+1=4\)
\(\Leftrightarrow x=1\)
Vậy ....