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a: \(1=4^0\)
\(4=4^1\)
\(16=4^2\)
\(256=4^4\)
b: \(\dfrac{1}{4}=4^{-1}\)
\(\dfrac{1}{64}=4^{-3}\)
\(\dfrac{1}{256}=4^{-4}\)
\(\dfrac{1}{16}=4^{-2}\)
\(\dfrac{1}{1024}=4^{-5}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
64\(^x\) : 16\(^x\) = 256
(64: 16)\(x\) = 256
4\(^x\) = 44
\(x\) = 4
Vậy \(x\) = 4
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\(64^x.16^x=256^{12}:1024\)
\(\Rightarrow\) \(\left(4^3\right)^x.\left(4^2\right)^x=\left(4^4\right)^{12}:4^5\)
\(\Rightarrow\) \(4^{3x}.4^{2x}=4^{48}:4^5\)
\(\Rightarrow\) \(4^{3x+2x}=4^{43}\)
\(\Rightarrow\) \(3x+2x=43\)
\(\Rightarrow\) \(\left(3+2\right)x=43\)
\(\Rightarrow\) \(5x=43\)
\(\Rightarrow\) \(x=\frac{43}{5}\)
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(-3/4)63x-1=(3/4)^3
3x-1=3+1
3x=3=1
x=4;3
x=4/3
Vậy x=4/3
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Bài 1:
a.
Ta có tỉ lệ thức: 4,5 x 14,4 = 6 x 10,8
\(\Rightarrow\frac{4,5}{6}=\frac{10,8}{14,4};\frac{4,5}{10,8}=\frac{6}{14,4};\frac{6}{4,5}=\frac{14,4}{10,8};\frac{10,8}{4,5}=\frac{14,4}{6}\)
b.
Ta có tỉ lệ thức 1: 4 x 1024 = 16 x 256
\(\Rightarrow\frac{4}{16}=\frac{256}{1024};\frac{4}{256}=\frac{16}{1024};\frac{16}{4}=\frac{1024}{256};\frac{256}{4}=\frac{1024}{16}\)
Ta có tỉ lệ thức 2: 16 x 64 = 4 x 256
\(\Rightarrow\frac{16}{4}=\frac{256}{64};\frac{16}{256}=\frac{4}{64};\frac{4}{16}=\frac{64}{256};\frac{256}{16}=\frac{64}{4}\)
Bài 2:
Áp dụng t/c DTSBN. ta có:
\(\frac{x}{11}=\frac{y}{7}=\frac{x+y}{11+7}=\frac{-54}{18}=-3\)
\(\Rightarrow x=11.\left(-3\right)=-33\)
\(\Rightarrow y=7.\left(-3\right)=-21\)
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\( {64^{x - 1}}:{4^{x + 1}} = {\left( {{{256}^x}} \right)^2}\\ \Leftrightarrow {4^{3x - 3}}:{4^{x + 1}} = {256^{2x}}\\ \Leftrightarrow {4^{2x - 4}} = {4^{8x}}\\ \Leftrightarrow 2x - 4 = 8x\\ \Leftrightarrow - 6x = 4\\ \Leftrightarrow x = - \dfrac{2}{3} \)
a) \(64^x:16^x=256\)
\(\Rightarrow\left(2^6\right)^x:\left(2^4\right)^x=2^8\)
\(\Rightarrow2^{6x}:2^{4x}=2^8\)
\(\Rightarrow2^{6x-4x}=2^8\)
\(\Rightarrow2^{2x}=2^8\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=4\)
b) \(\dfrac{-2401}{7^x}=-7\)
\(\Rightarrow\dfrac{-7^4}{7^x}=-7\)
\(\Rightarrow-7^{4-x}=-7\)
\(\Rightarrow7^{4-x}=7\)
\(\Rightarrow4-x=1\)
\(\Rightarrow x=4-1\)
\(\Rightarrow x=3\)
c) \(\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=\dfrac{64}{-256}\)
\(\Rightarrow\left(-4\right)^x=-4\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^1\)
\(\Rightarrow x=1\)
\(a) 64^x:16^x=256\\\Rightarrow (64:16)^x=256\\\Rightarrow 4^x=4^4\\\Rightarrow x=4\\---\)
\(b,\dfrac{-2401}{7^x}=-7\)
\(\Rightarrow7^x=-2401:\left(-7\right)\)
\(\Rightarrow7^x=343\)
\(\Rightarrow7^x=7^3\)
\(\Rightarrow x=3\)
\(c,\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=64:\left(-256\right)\)
\(\Rightarrow\left(-4\right)^x=-\dfrac{1}{4}\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^{-1}\)
\(\Rightarrow x=-1\)
#\(Toru\)