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a)\(\left(\frac{1}{2}-\frac{1}{3}\right).6^x+6^{x+2}=6^{15}+6^{18}\)
\(\frac{1}{6}.6^x+6^{x+2}=6^{15}\left(1+6^3\right)\)
\(\frac{1}{6}.6^x\left(1+6^3\right)=6^{15}.217\)
\(6^{x-1}.217=6^{15}.217\)
\(6^{x-1}=6^{15}\)
\(x-1=15\)
\(x=16\)
b) \(\left(\frac{1}{2}-\frac{1}{6}\right).3^{x+4}-4.3^x=3^{16}-4.3^{13}\)
\(\frac{1}{3}.3^x.4\left(3^4-1\right)=3^{13}.4\left(3^3-1\right)\)
\(3^x.4.\left(3^3-1\right)=3^{13}.4.\left(3^3-1\right)\)
\(3^x=3^{13}\)
\(x=13\)
\(\left(\frac{1}{2}-\frac{1}{6}\right).\left(3^x.3^4\right)-4.3^x=3^{16}-4.3^{13}\)
=> \(\frac{1}{3}.3^x.3^4-4.3^x=3^{16}-4.3^{13}\)
=> \(3^x.3^4-4.3^x=\left(3^{16}-4.3^{13}\right):\frac{1}{3}\)
=> \(3^x.3^4-4.3^x=-386339074,3\)
=> \(3^x.\left(3^4-4\right)=-386339074,3\)
=> \(3^x.77=-386339074,3\)
=> \(3^x=-386339074,3:77\)
=> \(3^x=-5017390,575\)
=> x = ... chắc tự ngồi tính đc
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a)\(\frac{1}{3}x+\frac{2}{5}\left(x-1\right)=0\)
\(\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)
\(\frac{11}{15}x-\frac{2}{5}=0\)
\(\frac{11}{15}x=\frac{2}{5}\)
\(x=\frac{6}{11}\)
b)(2x-3)(6-2x)=0
=>2x-3=0 hoặc 6-2x=0
=>x=3/2 hoặc x=3
c)\(x:\frac{3}{4}+\frac{1}{4}=-\frac{2}{3}\)
\(x:\frac{3}{4}=-\frac{11}{12}\)
\(x=-\frac{11}{16}\)
d)\(-\frac{2}{3}-\frac{1}{3}\left(2x-5\right)=\frac{3}{2}\)
\(-\frac{2}{3}-\frac{2}{3}x+\frac{5}{3}=\frac{3}{2}\)
\(-\frac{2}{3}x+1=\frac{3}{2}\)
\(-\frac{2}{3}x=\frac{1}{2}\)
\(x=-\frac{3}{4}\)
\(60\%x+\frac{2}{3}x=\frac{1}{3}.6\frac{1}{3}\)
\(\frac{3}{5}x+\frac{2}{3}x=\frac{19}{9}\)
\(\frac{19}{15}x=\frac{19}{9}\)
\(x=\frac{5}{3}\)
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a)=>(x-2)*6=(x+3)*5
6x-12=5x+15
6x-5x=15+12
x=27
b)=>(x+1)(2x+1)=-6*(-48)
x(2x+1)+2x+1=288
2x2+x+2x+1=288
2x2+3x=288-1
x(2x+1)=287
Ta xét bảng sau:
x | 1 | 7 | 41 | 287 | -1 | -7 | -41 | -287 |
2x+1 | 287 | 41 | 7 | 1 | -287 | -41 | -7 | -1 |
2x | 286 | 40 | 6 | 0 | -288 | -42 | -8 | -2 |
x | 143 | 20 | 3 | 0 | -144 | -21 | -4 | -1 |
=>Không có x nào thỏa mãn đề bài
a,=>(x-2).6=5.(x+3)
=>6x-12=5x+15
=>6x-5x=12+15
=>x=27
Vậy x=27
b,=>(x+1)(2x+1)=(-6).(-48)=288
=>x(2x+1)+1(2x+1)=288
=>2x^2+x+2x=288-1=287
=>2x^2+3x=287
=>...
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\(27.3^x=3^6\)
\(3^3.3^x=3^6\)
\(3^{3+x}=3^6\)
\(\Rightarrow3+x=6\Rightarrow x=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
c. khi và chỉ khi \(\frac{3}{5}\cdot\frac{1}{x}=\frac{1}{3}-\frac{4}{15}=\frac{1}{15}\)
\(\frac{1}{x}=\frac{1}{15}\cdot\frac{5}{3}=\frac{1}{9}\)
suy ra x=9
a,7/6x=3/5-1/30
7/6x=17/30
x=17/30:7/6
x=17/35
b,(-9/2-2x).11/7=11/4
-9/2-2x=11/4:11/7
-9/2-2x=7/4
2x=-9/2-7/4
2x=-25/4
x=-25/4:2
x=-25/8
c,9
d,x=-2
e,2.8=x.x=x2
16=x2=>x=4 hoặc -4
`150:(x+6)=3`
`x+6=150:3`
`x+6=50`
`x=50-6`
`x=44`
150:(x+6)=3150:(x+6)=3
x+6=150:3x+6=150:3
x+6=50x+6=50
x=50−6x=50-6
x=44