Bài 1: tìm x
a) 2^2x.2^4=1024
b) 2.3^x=10.3^12+8.27^4
c) 5^8.25^x+1=5^17
d) 3^x-1+3^x-4=28.243
e) (2x-4)^5=(2x-4)^3
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tìm số tự nhiên x biết
a)2^x-15=17
b)(7^x-11)^3=2^5.5^2+200
c)2.3^x=10.3^12+8.27^4
d)(2x-150^5=(2x-15)^3
2\(^x\)- 15 = 17
\(\Rightarrow\)2\(^x\) = 32
\(\Rightarrow\)x = 5
Số số hạng là :
(2x - 2) : 2 + 1 = x - 1 + 1 = x (số)
Tổng là :
(2x + 2).x : 2 = 210
=> (2x2 + 2x) : 2 = 210
=> x2 + x = 210
=> x(x + 1) = 210
=> x(x + 1) = 20.21
=> x = 20
Vậy x = 20
Ta có : \(\frac{x}{2}=\frac{10}{x+1}\)
=> x(x + 1) = 10.2
=> x(x + 1) = 20
=> sai đề
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, 7\(x\) - \(x\) = 521 : 519 + 3.22.7
6\(x\) = 53 + 3.4.7
6\(x\) = 125 + 12.7
6\(x\) = 125 + 84
6\(x\) = 209
\(x\) = 209 : 6
\(x\) = \(\dfrac{209}{6}\)
b; 11\(x\) - 7\(x\) + 34 : 33 = 54 + 2\(x\)
4\(x\) + 3 = 625 + 2\(x\)
4\(x\) - 2\(x\) = 625 - 3
2\(x\) = 622
\(x\) = 622 : 2
\(x\) = 311
c; 75 - 5.(\(x-3\))3 = 700
5.(\(x\) - 3)3 = 700 - 75
5.(\(x\) - 3)3 = - 625
(\(x\) - 30)3 = - 625 : 5
(\(x\) - 30)3 = - 125
(\(x-3\))3 = (-5)3
\(x\) - 3 = - 5
\(x\) = - 5 + 3
\(x\) = -2
d, 3.(2\(x\) - 1)2 = 75
(2\(x\) - 1)2 = 75 : 3
(2\(x\) - 1)2 = 25
\(\left[{}\begin{matrix}2x-1=-5\\2x-1=5\end{matrix}\right.\)
\(\left[{}\begin{matrix}2x=-5+1\\2x=5+1\end{matrix}\right.\)
\(\left[{}\begin{matrix}2x=-4\\2x=6\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)
k,(x + 1) + (x + 2) + (x + 3) + .... + (x + 100) = 5750
=> 100x + (1 + 2 + 3 + ... + 100) = 5750
=> 100x + 5050 = 5750
=> 100x = 5750 - 5050
=> 100x = 700
=> x = 700 : 100
=> x = 7
i,92.4 - 27 = (x + 350) : x + 315
=> 1 + 350 : x + 315 = 341
=> 350 : x = 341 - 316 = 25
-> x = 350: 25 = 14
a) \(2^{2x}.2^4=1024\)
\(2^{2x}=1024:2^4\)
\(2^{2x}=1024:16\)
\(2^{2x}=64\)
\(2^{2x}=2^6\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
vay \(x=3\)
b) \(2.3^x=10.3^{12}+8.27^4\)
\(2.3^x=2.5.3^{12}+2^3.\left(3^3\right)^4\)
\(2.3^x=2.5.3^{12}+2^3.3^{12}\)
\(2.3^x=2.3^{12}.\left(5+2^2\right)\)
\(2.3^x=2.3^{12}.9\)
\(2.3^x=2.3^{12}.3^2\)
\(2.3^x=2.3^{14}\)
\(\Rightarrow x=14\)
vay \(x=14\)
c) \(5^8.25^x+1=5^{17}\)
\(5^8.\left(5^2\right)^x+1=5^{17}\)
\(5^8.5^{2x}+1=5^{17}\)
\(5^{8+2x}=5^{17}-1\)
e) \(\left(2x-4\right)^5=\left(2x-4\right)^3\)
\(\left(2x-4\right)^5-\left(2x-4\right)^3=0\)
\(\left(2x-4\right)\left[\left(2x-4\right)^2-1\right]=0\)
\(\left(2x-4\right)\left(2x-4-1\right)\left(2x-4+1\right)=0\)
\(\left(2x-4\right)\left(2x-5\right)\left(2x-3\right)=0\)
\(\Rightarrow2x-4=0\)hoac \(\orbr{\begin{cases}2x-5=0\\2x-3=0\end{cases}}\)
\(\Rightarrow2x=4\)hoac \(\orbr{\begin{cases}2x=5\\2x=3\end{cases}}\)
\(\Rightarrow x=2\)hoac \(\orbr{\begin{cases}x=\frac{5}{2}\\x=\frac{3}{2}\end{cases}}\)
vay \(x=2\)hoac \(\orbr{\begin{cases}x=\frac{5}{2}\\x=\frac{3}{2}\end{cases}}\)