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a)\(5x\cdot5x\cdot5x=\left(5x\right)^3\)
b) \(x^1\cdot x^2\cdot...\cdot x^{2006}=x^{1+2+3+...+2006}=x^{2013021}\)
c)\(x\cdot x^4\cdot x^7\cdot...\cdot x^{100}=x^{1+4+7+...+100}=x^{101\cdot17}=x^{1717}\)
a) 2x = 64
=> 2x = 26
=> x = 6
b) 5x = 7x
=> 7x - 5x = 0
=> 5x(2x - 1) = 0
=> \(\orbr{\begin{cases}5^x=0\\2^x-1=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x\in\varnothing\\2^x=1\end{cases}}\)\(\Rightarrow2^x=2^0\Rightarrow x=0\)
c) 5x . 53 = 125
=> 5x + 3 = 53
=> x + 3 = 3
=> x = 0
d) 3x - 17 = 64
=> 3x = 64 + 17
=> 3x = 81
=> 3x = 34
=> x = 4
e) (3x - 5)3 = 52 . 24 + 600
=> (3x - 5)3 = 25.16 + 600
=> (3x - 5)3 = 400+ 600
=> (3x - 5)3 = 1000
=> (3x - 5)3 = 103
=> 3x - 5 = 10
=> 3x = 15
=> x = 15 : 3
=> x = 5
g) (5x - 15)3 = (5x - 15)7
=> (5x - 15)7 - (5x - 15)3 = 0
=> (5x - 15)3. [(5x - 15)4 - 1] = 0
=> \(\orbr{\begin{cases}\left(5x-15\right)^3=0\\\left(5x-15\right)^4-1=0\end{cases}\Rightarrow\orbr{\begin{cases}\left(5x-15\right)=0\\\left(5x-15\right)^4=1\end{cases}\Rightarrow}\orbr{\begin{cases}5x-15=0\\5x-15=\pm1\end{cases}}}\)
Nếu 5x - 15 =0
=> 5x = 15
=> x = 3
Nếu 5x - 15 = 1
=> 5x = 16
=> x = 16 : 5
=> x = 16/5
Nếu 5x - 16 = -1
=> 5x = 14
=> x = 14 : 5
=> x = 14/5
Vậy \(x\in\left\{3;\frac{16}{5};\frac{14}{5}\right\}\)
a) 2x = 64
Vì 26 = 64 nên x = 6
Vậy x = 6
b) 5x = 7x
Vì 50 = 1 và 70 = 1
=> x = 0
Vậy, x = 0
c) 5x . 53 = 625
Ta có 625 = 54
nên 5x . 53 = 54
5x+3 = 54
=> x = 1
Vậy x = 1
d) 3x - 17 = 64
3x = 64 + 17 = 81 = 34
=> x = 4
Vậy x = 4
e) ( 3x - 5 ) 3 = 52 . 24 + 600
( 3x - 5 ) 3 = 25 . 16 + 600 = 1000 = 103
=> 3x - 5 = 10
3x = 10 + 5 = 15
x = 15 : 3 = 5
Vậy x = 5
g) ( 5x - 15 ) 3 = ( 5x - 15 ) 7
=> (5x - 15 ) 3 : ( 5x - 15 ) 7 = 1
( 5x - 15 ) 3 - 7 = 1
( 5x - 15 ) -4 = 1 = 1-4 = -1-4
=> 5x - 15 = 1 hoặc 5x - 15 = -1
5x = 1 + 15 hoặc 5x = -1 + 15
5x = 16 hoặc 5x = 14
\(x=\frac{16}{5}\) hoặc \(x=\frac{14}{5}\)
Vậy, \(x\in\left\{\frac{16}{5};\frac{14}{5}\right\}\)
Cbht
a) 52 . x = 62 + 82
\(5^2\cdot x=36+64\)
\(5^2\cdot x=100\)
\(x=100\div5^2\)
\(x=100\div25\)
\(x=4\)
b) ( 22 + 42 ) . x + 24 . 5 . x = 102
\(\left(4+16\right)\cdot x+16\cdot5\cdot x=100\)
\(x\cdot\left(20+80\right)=100\)
\(x\cdot100=100\)
\(x=100\div100\)
\(x=1\)
c ) 24 . x = 26
\(x=2^6\div2^4\)
\(x=2^{6-4}\)
\(x=2^2\)
\(x=4\)
d) 33 . x + 23 . x = 102
\(x\cdot\left(23+27\right)=100\)
\(x\cdot50=100\)
\(x=100\div50\)
\(x=2\)
e) 78 . x = 710
\(x=7^{10}\div7^8\)
\(x=7^{10-8}\)
\(x=7^2\)
\(x=49\)
a) 3x.3 = 243
3x + 1 = 35
x + 1 = 5
x = 4
b) x2 = x
x2 - x = 0
x(x - 1) = 0
x = 0 hoặc x - 1 = 0
x = 1
d) 64.4x = 16
4x = 16 : 64
4x = 1/4
4x = 4-1
x = -1
Bài 1 :
a/ \(a^3.a^9=a^{3+9}=a^{12}\)
b/\(\left(a^5\right)^7=a^{5.7}=a^{35}\)
c/ \(\left(a^6\right).4.a^{12}=a^{24}.a^{12}.4=a^{24+12}.4=a^{36}.4\)
d/ \(\left(2^3\right)^5.\left(2^3\right)^3=2^{15}.2^9=2^{15+9}=2^{24}\)
e/ \(5^6:5^3+3^3.3^2\)
\(=5^3+3^5=125+243=368\)
i/ \(4.5^2-2.3^2\)
\(=2^2.5^2-2.3^2\)
\(=2^2.25-2^2.14\)
\(=2^2.\left(25-14\right)\)
\(=2^2.11\)
\(=4.11=44\)
Bài 3:
a. 5x.5x.5x = 5x3
b.x1.x2......x2006 = x1+2+..+2006
c.x.x4.x7....x100 = x1+4+7+...+100
d.x2.x5.x8....x2003 = x2+5+8+..+2003
Bài 3 :
a) 5x . 5x . 5x = ( 5x )3
b) x1 . x2 . ... . x2006
= x1+2+3+...+2006
= x(2006+1).2006:2
= x2013021
c) x . x4 . x7 . ... . x100
= x1+4+7+...+100
= x(100+1).34:2
= x1717
d) x2 . x5 . x8 . ... . x2003
= x2+5+8+...+2003
= x(2003+2).668:2
= x669670
V )x+(x+1)+(x+2)+....+(x+30)=1240
31 . x + (1 + 2 + 3 + 4 +...+ 29 + 30) = 1240
31 . x + 31.15 = 1240
31 . x = 1240 - 31.15
31 . x = 775
x = 775 : 31
x = 25
a. 5x.5x.5x
= (5x)3
Học tốt nhé!!!
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