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Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
\(\frac{x-1}{2018}+\frac{x-7}{503}=\frac{x-3}{1008}+\frac{x-9}{670}\)
\(\Leftrightarrow\frac{x-1}{2018}-1+\frac{x-7}{503}-4=\frac{x-3}{1008}-2+\frac{x-9}{670}-3\)
\(\Leftrightarrow\left(x-2019\right)\left(\frac{1}{2018}+\frac{1}{503}-\frac{1}{1008}-\frac{1}{670}\right)=0\)
\(\Rightarrow x=2019\)
#CBHT
Đặt A =1/2+1/4+1/8+...+1/1024
2A= 1+1/2+1/4+...+1/512
A= 1-1/1024
=>A<1hay ...
Ta có:
a) \(\Leftrightarrow3\left(x+2\right)=-4\left(x-5\right)\)
\(\Leftrightarrow3x+6=-4x+20\)
\(\Leftrightarrow7x=14\Leftrightarrow x=2\)
a, \(2.x^x=10.3^{12}+8.27^4\)
\(2.x^x=10.3^{12}+8.3^{12}\)
\(2.x^x=3^{12}.\left(10+8\right)\)
\(2.x^x=3^{12}.18\)
\(2.x^x=3^{12}.2.3^3\)
\(2.x^x=3^{15}.2\)
\(x^x=3^{15}\)( Hình như sai đề )
b,\(3^{2x+2}=9^{x+3}\)
\(3^{2x+2}=3^{2x+3}\)
a/ \(\frac{x+2}{27}=\frac{x}{9}\)
=> 9(x + 2) = 27x
=> 9x + 18 = 27x
=> 9x + 18 - 27x = 0
=> 9x - 27x + 18 = 0
=> -18x = -18
=> x = 1
b/ \(\frac{-7}{x}=\frac{21}{34-x}\)
=> -7(34 - x) = 21x
=> -238 + 7x = 21x
=> 21x - 7x = -238
=> -14x = 238
=> x = -17
c) \(\frac{-8}{15}< \frac{x}{40}< \frac{-7}{15}\)
Ta có BCNN(15,40,15) = 120
=> \(\frac{-64}{120}< \frac{3x}{120}< \frac{-56}{120}\)
=> -64 < 3x < -56
=> x \(\in\){ -19;-20;-21}
Câu d tương tự
a) 3x = 81 b) 2x . 16 = 128 c) 3x : 9 = 27 d) x4 = x
3x = 34 2x = 128 : 16 3x = 27 : 9 => x = 1
=> x = 4 2x = 8 3x = 3 Vậy x= 1
Vậy x = 4 x = 4 => x = 1
Vậy x = 4 Vậy x = 1
e) ( 2x + 1 )3 = 27
( 2x + 1 )3 = 33
=> 2x + 1 = 3
2x = 3 - 1
2x = 2
x = 1
Vậy x = 1
a, 3x=81 b, 2x*16=128 c, 3x:9=27 d, x4=x
=> 3x=34 => 2x=128:16 => 3x=27.9 => x=0 hoặc x=1
=> x=4 => 2x=8 => 3x=243
=> x=4 => 3x=35
=> x=5
e, (2x+1)3=27 f, (x-2)2=(x-2)4
=> (2x+1)3=33 +, TH1: x-2=1 => (x-2)2=(x-2)4=1 => x-2=x-2=1 => x=3
=> 2x+1=3 +, TH2: x-2=0 => (x-2)2=(x-2)4=0 => x-2=x-2=0 => x=2
=> 2x=2
=> x=2:2
=> x=1
g, 25 <= 5x < 625
=> 52 <= 5x < 54
=> x={2;3}
a, \(2\cdot2^2\cdot2^3\cdot2^4\cdot...\cdot2^x=1024\)
\(\Leftrightarrow2^{1+2+3+4+...+x}=2^{10}\Leftrightarrow1+2+3+4+...+x=10\)
\(\Rightarrow\left(x+1\right)x\div2=10\Rightarrow\left(x+1\right)x=20\)
Vì : ( x + 1 ) x là hai số tự nhiên liên tiếp \(\Rightarrow x=4\in Z\)
Vậy x = 4
b, \(9.27< 3^x< 243\Leftrightarrow3^5< 3^x< 3^5\)
\(\Rightarrow5< x< 5\Rightarrow x\in\varnothing\)
Vậy \(x\in\varnothing\)