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a)=3^4<3.n<3^10
=>n=4;5;6;7;8;9
b)5^2<5^n-1<5^4
=>n-1=3=>n=4
c)5.5^2n==5^6
=>5^2n+1=5^6
=>n=7/2
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{5^{x+1}}{125}=\dfrac{1}{25^{x-2}}\\ \dfrac{5^{x+1}}{125}=\dfrac{1}{5^{2x-4}}\\ 5^{x+1}\cdot5^{2x-4}=125\\ 5^{x+1+2x-4}=5^3\\ 5^{\left(x+2x\right)+\left(1-4\right)}=5^3\\ 5^{3x-3}=5^3\\ 3x-3=3\\ 3x=6\\ x=2\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\dfrac{1}{2}\right)^3.\left(-2\right)^2-25\%+\dfrac{3}{5}.25-30\\ =\dfrac{1}{2}.\left(\dfrac{1}{2}\right)^2.\left(-2\right)^2-\dfrac{25}{100}+\dfrac{3}{5}.25-30\\ =\left(\dfrac{1}{2}\right).\left[\dfrac{1}{2}.\left(-2\right)\right]^2-\dfrac{1}{4}+15-30\\ =\dfrac{1}{2}.\left(-1\right)^2-\dfrac{1}{4}+15-30\\ =\dfrac{1}{2}-\dfrac{1}{4}+15-30\\ =\dfrac{1}{4}+15-30=\dfrac{61}{4}-30=-\dfrac{59}{4}\)
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=1,3125
giúp tớ nhé ,tớ mới bị từ 290
ai giúp mình mình giúp lại
cảm ơn trước
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\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x\left(x+3\right)}=\frac{125}{376}\)
=>\(3\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{x\left(x+3\right)}\right)=3.\frac{125}{376}\)
=>\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{x\left(x+3\right)}=\frac{375}{376}\)
=>\(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{x}-\frac{1}{x+3}=\frac{375}{376}\)
=>\(1-\frac{1}{x+3}=\frac{375}{376}\)
=>\(\frac{1}{x+3}=1-\frac{375}{376}\)
=>\(\frac{1}{x+3}=\frac{1}{376}\)
=>x+3=376
=>x=376-3
=>x=373
Vậy x=373
![](https://rs.olm.vn/images/avt/0.png?1311)
b) Ta có: \(-5+\left|3x-1\right|+6=\left|-4\right|\)
\(\Leftrightarrow\left|3x+1\right|+1=4\)
\(\Leftrightarrow\left|3x+1\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}3x+1=3\\3x+1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=2\\3x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{\dfrac{2}{3};-\dfrac{4}{3}\right\}\)
c) Ta có: \(\left(x-1\right)^2=\left(x-1\right)^4\)
\(\Leftrightarrow\left(x-1\right)^2-\left(x-1\right)^4=0\)
\(\Leftrightarrow\left(x-1\right)^4-\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)^2\cdot\left[\left(x-1\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2\cdot\left(x-1-1\right)\left(x-1+1\right)=0\)
\(\Leftrightarrow x\cdot\left(x-1\right)^2\cdot\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=2\end{matrix}\right.\)
Vậy: \(x\in\left\{0;1;2\right\}\)
d) Ta có: \(5^{-1}\cdot25^x=125\)
\(\Leftrightarrow5^{-1}\cdot5^{2x}=5^3\)
\(\Leftrightarrow5^{2x-1}=5^3\)
\(\Leftrightarrow2x-1=3\)
\(\Leftrightarrow2x=4\)
hay x=2
Vậy: x=2
=>5.(52)x+1=(53)x
=>5.52x+2=53x
=>52x+2+1=53x
=>2x+2+1=3x
=>3=3x-2x
=>x.(3-2)=3
=>x=3
5.25^x+1=125^x
5(5^2)^x+1=(5^3)^x
5.5^2x+2=5^3x
5^2x+2+1=5^3x
suy ra 2x+3=3x
2x-3x=-3
-x=-3
x=3