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Ta có: 3x +3x+1+3x+2= 3x x 30 +3x x 31 +3x x 32=1053
Suy ra: 3x x(30+31+32)=3x x(1+3+9)=3x x 13=1053
Suy ra: 3x =1053:13=81
Mà 34 = 81
Vậy x = 4
( 2x + 1 )5 : ( 2x + 1 )2 = 1
\(\Rightarrow\)( 2x+ 1 )3 = 1 = 13
\(\Rightarrow\)2x + 1 = 1
\(\Rightarrow\)2x = 0
\(\Rightarrow\)x = 0
2x + 2 . 2x + ... + 10 . 2x= 10 . 11
\(\Rightarrow\)2x . ( 1 + 2 + 3 + ... + 9 + 10 ) = 110
\(\Rightarrow\)2x . 55 = 110
\(\Rightarrow\)2x = 110 : 55
\(\Rightarrow\)2x = 2
\(\Rightarrow\)x = 1
b) \(\Leftrightarrow18x-288=27.4+8.9-144\)
\(\Leftrightarrow18x=108+72-144+288=324\)
\(\Leftrightarrow x=18\)
2.2.2.5.5.5.10 = ( 2.5 ) . ( 2.5 ) . ( 2.5 ) . 10 = 10 . 10 . 10 . 10 = 104
2 . 2 . 2 . 2 . 4 . 4 = ( 2.2 ) . ( 2.2 ) . 4 . 4 = 4 . 4 . 4 . 4 = 44
4 . 4 . 8 . 8 = (2 . 2 ) . ( 2.2 ) . ( 2 . 2 . 2 ) . ( 2. 2 . 2 ) = 2 . 2 .2 . 2 .2 . 2 .2 . 2 .2 . 2 = 210
x3 = 125
x = \(\sqrt[3]{125}=5\)
2x + 4.2x = 5.25
2x ( 4 + 1 ) = 25 . 5
2x . 5 = 25 . 5
x = 5
3n : 9 = 37
3n : 32 = 37
3n-2 = 37
n - 2 = 7
n = 7 + 2 = 9
n = { 3 ; 4 ; 5 }
\(x^2-3x+2=6\Rightarrow x^2-2x-x+2=6\Rightarrow x\left(x-2\right)-\left(x-2\right)=6\)
\(\Rightarrow\left(x-1\right)\left(x-2\right)=6\) Vì x-1>x-2 nên ta có bảng:
| x-1 | -1 | -2 | 6 | 3 |
| x-2 | -6 | -3 | 1 | 2 |
| x | 0 và 4(loại) | -1(TM) | 7 và 3 | 4(TM) |
Vậy x\(\in\left\{-1,1\right\}\)
2 - 3x + 2 = 6
\(\Rightarrow\)2 - 3x = 6 - 2
\(\Rightarrow\)2 - 3x = 4
\(\Rightarrow\)3x = 4 + 2
\(\Rightarrow\)3x = 6
\(\Rightarrow\)x = 6 : 3
\(\Rightarrow\)x = 2
vậy x = 2
Bài 1:
a) \(8^5\cdot8^2=8^7\)
b) \(9^3\cdot3^2=\left(3^2\right)^3\cdot3^2=3^6\cdot3^2=3^8\)
c) \(2^7\cdot5^7=10^7\)
d) \(27^6:3^3=\left(3^3\right)^6:3^3=3^{18}:3^3=3^{15}\)
Bài 2:
a) \(x^6:x^3=125\)
\(\Rightarrow x^3=125\)
\(\Rightarrow x=5\)
b) \(x^{20}=x\)
\(\Rightarrow x^{20}-x=0\)
\(\Rightarrow x\left(x^{19}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{19}-1=0\Rightarrow x=1\end{matrix}\right.\)
c) \(3^x\cdot3=243\)
\(\Rightarrow3^x=81\)
\(\Rightarrow x=4\)
d) \(2x-138=2^3\cdot3^2\)
\(\Rightarrow2x-138=72\)
\(\Rightarrow2x=200\)
\(\Rightarrow x=100\)
Giải:
Bài 1:
a) \(8^5.8^2=8^{5+2}=8^7\)
b) \(9^3.3^2=3^6.3^2=3^{6+2}=3^8\)
c) \(2^7.5^7=\left(2.5\right)^7=10^7\)
d) \(27^6:3^3=3^{18}:3^3=3^{18-3}=3^{15}\)
Bài 2:
a) \(x^6:x^3=x^{6-3}=x^3=125\)
\(\Leftrightarrow x=5\)
b) \(x^{20}=x\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\\x=1\end{matrix}\right.\)
c) \(3^x.3=243\)
\(\Leftrightarrow3^{x+1}=243\)
\(\Leftrightarrow3^{x+1}=3^5\)
\(\Leftrightarrow x+1=5\Leftrightarrow x=4\)
d) \(2.x-138=2^3.3^2\)
\(\Leftrightarrow2.x-138=8.9\)
\(\Leftrightarrow2.x-138=72\)
\(\Leftrightarrow2.x=72+138\)
\(\Leftrightarrow2.x=210\Leftrightarrow x=105\)
Chúc bạn học tốt!