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4:
=>(2x+3,5)=7/12*3/14=21/168=1/8
=>2x=1/8-7/2=1/8-28/8=-27/8
=>x=-27/16
5: =>1/3:3x=-21/4
=>3x=-1/3:21/4=-1/3*4/21=-4/63
=>x=-4/189
6: =>2+7/9-3/4(x+1)=7/9
=>2-3/4(x+1)=0
=>3/4(x+1)=2
=>x+1=2:3/4=2*4/3=8/3
=>x=5/3
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)+(x+2)+(x+3)+...+(x+9)+(x+10)=56
⇒ x.10+(1+2+3+...+9+10)=56
⇒ x.10+[(10+1).10:2] = 56
⇒ x.10+55=56
⇒ x.10 = 56-55 = 1
⇒ x = 1:10=0,1
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
(x+1)+(x+2)+(x+3)+...+(x+9)+(x+10)=56
⇒ x.10+(1+2+3+...+9+10)=56
⇒ x.10+[(10+1).10:2] = 56
⇒ x.10+55=56
⇒ x.10 = 56-55 = 1
⇒ x = 1:10=0,1
(\(x+1\)) + (\(x+2\)) + (\(x\) + 3)+...+ (\(x\) + 10) = 56
xét dãy số \(x+1;x+2;x+3;...;x+10\)
Dãy số trên có khoảng cách là: \(x+2-x-1\) = 1
Dãy số trên có số số hạng là: (\(x+10-x-1\)) : 1 + 1 = 10
Vậy:
(\(x+1\))+(\(x+2\))+(\(x+3\))+...+(\(x+10\)) = (\(x+10\) + \(x+1\)).10 : 2
⇒(2\(x\) + 11).5 = 56
2\(x\) + 11 = 56 : 5
2\(x\) + 11 = 11,2
2\(x\) = 11,2 - 11
2\(x\) = 0,2
\(x\) = 0,2 : 2
\(x\) = 0,1
![](https://rs.olm.vn/images/avt/0.png?1311)
Cho mk sửa lại ở câu c là 2^n+2 + 2^n+1 - 2^n = 56 nha!
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{x}{3\frac{1}{2}.2\frac{2}{3}}=\frac{9}{56}\Rightarrow\frac{x}{\frac{7}{2}.\frac{8}{3}}=\frac{9}{56}\Rightarrow x=\frac{9}{56}.\frac{28}{3}=\frac{3}{2}\)
\(x:\left(3\frac{1}{2}.2\frac{2}{3}\right)=\frac{9}{56}\)
\(x:\left(\frac{7}{2}.\frac{8}{3}\right)=\frac{9}{56}\)
\(x:\left(\frac{7.4}{3}\right)=\frac{9}{56}\)
\(x.\frac{3}{28}=\frac{9}{56}\)
\(x=\frac{9}{56}.\frac{28}{3}=\frac{3}{2}\)
Vậy \(x=\frac{3}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: =>3^x=81
=>x=4
2: =>2^x=8
=>x=3
3: =>x^3=2^3
=>x=2
4: =>x^20-x=0
=>x(x^19-1)=0
=>x=0 hoặc x=1
5: =>2^x=32
=>x=5
6: =>(2x+1)^3=9^3
=>2x+1=9
=>2x=8
=>x=4
7: =>x^3=115
=>\(x=\sqrt[3]{115}\)
8: =>(2x-15)^5-(2x-15)^3=0
=>(2x-15)^3*[(2x-15)^2-1]=0
=>2x-15=0 hoặc (2x-15)^2-1=0
=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1
=>x=15/2 hoặc x=8 hoặc x=7
1. Tìm số tự nhiên x biết:
1) \(3^x.3=243\)
\(3^x=243:3\)
\(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
_____
2) \(7.2^x=56\)
\(2^x=56:7\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
_____
3) \(x^3=8\)
\(x^3=2^3\)
\(\Rightarrow x=3\)
_____
4) \(x^{20}=x\)
\(x^{20}-x=0\)
\(x\left(x^{19}-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x=1\)
5) \(2^x-15=17\)
\(2^x=17+15\)
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
_____
6) \(\left(2x+1\right)^3=9.81\)
\(\left(2x+1\right)^3=729=9^3\)
\(\rightarrow2x+1=9\)
\(2x=9-1\)
\(2x=8\)
\(x=8:2\)
\(\Rightarrow x=4\)
_____
7) \(x^6:x^3=125\)
\(x^3=125\)
\(x^3=5^3\)
\(\Rightarrow x=5\)
_____
8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)
_____
9) \(3^{x+2}-5.3^x=36\)
\(3^x.\left(3^2-5\right)=36\)
\(3^x.\left(9-5\right)=36\)
\(3^x.4=36\)
\(3^x=36:4\)
\(3^x=9\)
\(3^x=3^2\)
\(\Rightarrow x=2\)
_____
10) \(7.4^{x-1}+4^{x+1}=23\)
\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)
\(4^{x-1}.\left(7+4^2\right)=23\)
\(4^{x-1}.\left(7+16\right)=23\)
\(4^{x-1}.23=23\)
\(4^{x-1}=23:23\)
\(4^{x-1}=1\)
\(4^{x-1}=4^1\)
\(\rightarrow x-1=0\)
\(x=0+1\)
\(\Rightarrow x=1\)
Chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
a)\(x=\left(\dfrac{3}{56}\cdot\dfrac{28}{9}\right):\dfrac{-3}{7}=\dfrac{1}{6}:\dfrac{-3}{7}=-\dfrac{7}{18}\)
b)\(x=\left(\dfrac{7}{15}\cdot\dfrac{5}{3}\right)+\dfrac{3}{16}=\dfrac{7}{9}+\dfrac{3}{16}=\dfrac{139}{144}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\frac{62}{7}:x=\frac{29}{9}:\frac{3}{56}\)
\(\frac{62}{7}:x=\frac{1624}{27}\)
\(x=\frac{62}{7}:\frac{1624}{27}=\frac{837}{5684}\)
\(b,\frac{1}{5}:x=\frac{1}{5}-\frac{1}{7}\)
\(\frac{1}{5}:x=\frac{2}{35}\)
\(x=\frac{1}{5}:\frac{2}{35}=\frac{7}{2}\)
\(c,\frac{2}{3}.x-\frac{4}{7}=\frac{1}{7}\)
\(\frac{2}{3}.x=\frac{1}{7}+\frac{4}{7}=\frac{5}{7}\)
\(x=\frac{5}{7}:\frac{2}{3}=\frac{15}{14}\)
\(d,\frac{2}{7}-\frac{8}{9}.x=\frac{2}{3}\)
\(\frac{8}{9}.x=\frac{2}{7}-\frac{2}{3}=-\frac{8}{21}\)
\(x=-\frac{8}{21}:\frac{8}{9}=-\frac{3}{7}\)
\(e,\frac{4}{7}+\frac{5}{9}:x=\frac{1}{5}\)
\(\frac{5}{9}:x=\frac{1}{5}-\frac{4}{7}=-\frac{13}{35}\)
\(x=\frac{5}{9}:-\frac{13}{35}=\frac{175}{117}\)
\(i,\frac{2}{5}-\frac{2}{5}.x=\frac{2}{5}\)
\(\frac{2}{5}.\left(1-x\right)=\frac{2}{5}\)
\(1-x=\frac{2}{5}:\frac{2}{5}=1\)
\(x=1-1=0\)
\(g,\frac{2}{3}+\frac{1}{3}:x=-1\)
\(\frac{1}{3}:x=-1-\frac{2}{3}=-\frac{5}{3}\)
\(x=\frac{1}{3}:-\frac{5}{3}=-\frac{1}{5}\)
học tốt nha