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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) \(\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=\dfrac{64}{-256}\)
\(\Rightarrow\left(-4\right)^x=-4\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^1\)
\(\Rightarrow x=1\)
\(a) 64^x:16^x=256\\\Rightarrow (64:16)^x=256\\\Rightarrow 4^x=4^4\\\Rightarrow x=4\\---\)
\(b,\dfrac{-2401}{7^x}=-7\)
\(\Rightarrow7^x=-2401:\left(-7\right)\)
\(\Rightarrow7^x=343\)
\(\Rightarrow7^x=7^3\)
\(\Rightarrow x=3\)
\(c,\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=64:\left(-256\right)\)
\(\Rightarrow\left(-4\right)^x=-\dfrac{1}{4}\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^{-1}\)
\(\Rightarrow x=-1\)
#\(Toru\)
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1 Tinh
89/16+25(9/16÷125/64)÷(-27/8)
= \(\frac{89}{16}+25\left(\frac{9}{16}:\frac{125}{64}\right):-\frac{27}{8}\)
=\(\frac{89}{16}+\frac{25.36}{125}:-\frac{27}{8}\)
=\(\frac{89}{16}-\frac{32}{15}=\frac{823}{240}\)
\(\frac{89}{16}+25.\left(\frac{9}{16}:\frac{125}{64}\right):\left(\frac{-27}{8}\right)\)
=\(\frac{89}{16}+25.\frac{36}{125}:\left(\frac{-27}{8}\right)\)
=\(\frac{89}{16}+\frac{36}{5}:\left(\frac{-27}{8}\right)\)
=\(\frac{89}{16}+\left(\frac{-32}{15}\right)\)
=\(\frac{823}{240}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(16< 8^n< 64\)
\(\Rightarrow2^4< \left(2^3\right)^n< 2^6\)
\(\Rightarrow2^4< 2^{3n}< 2^6\)
\(\Rightarrow4< 3n< 6\)
\(\Rightarrow\dfrac{4}{3}< n< 2\)
![](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
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\dfrac{4^9.36+64^4}{16^4.100}=\dfrac{4^9.36+4^{12}}{4^9.25}=\dfrac{4^9\left(36+4^3\right)}{4^9.25}=\dfrac{100}{25}=4\)
`64^5:16^5`
`= (64:16)^5`
`= 4^5`
`= 1024`
1024
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