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a) 2^x.2^4=128
=>2^x.2^2=2^7
=>2^x=2^7:2^2
=>2^x=2^5
=>x=5
b)x^15=x
=>x^15-x=0
=>x(x^16-x)=0
=>2 trượng hợp:x=0 và x^16-1=0(x^16-1=0 cx 2 th nha)
b),d),e) như nhau nha!
c) dễ rồi
\(a)2^x\cdot4=128\)
\(\Rightarrow2^x=\frac{128}{4}\)
\(\Rightarrow2^x=32\)
\(\Rightarrow2^x=2^5\)
\(\Rightarrow x=5\)
\(b)x^{15}=x\)
\(\Rightarrow x^{15}-x=0\)
\(\Rightarrow x(x^{14}-1)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}-1=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=0\\x^{14}=1\end{cases}\Rightarrow}\hept{\begin{cases}x=0\\x=1\end{cases}}\)
\(c)(2x+1)^3=125\)
\(\Rightarrow(2x+1)^3=5^3\)
\(\Rightarrow2x+1=5\)
\(\Rightarrow2x=5-1\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=4:2=2\)
\(d)(x-5)^4=(x-5)^6\)
\(\Rightarrow(x-5)^6-(x-5)^4=0\)
\(\Rightarrow(x-5)^4\cdot\left[(x-5)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}(x-5)^4=0\\(x-5)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=6\end{cases}}\)
\(e)(2x-15)^5=(2x-15)^3\)
\(\Rightarrow(2x-15)^5-(2x-15)^3=0\)
\(\Rightarrow(2x-15)^3-\left[(2x-15)^2-1\right]=0\)
\(\Rightarrow\orbr{\begin{cases}(2x-15)^3=0\\(2x-15)^2-1=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\varnothing\\x=8\end{cases}}\)
Chúc bạn hoc tốt :>
a) 2x - 15 = 17
2x = 25
b) ( 7x - 11 )3 = 25. 52 + 200
(7x - 11)3 = 32 . 25 + 200
(7x -11)3 = 1000
(7x-11)3 = 103
7x - 11 = 10
7x = 10+11
7x = 21
x = 21 : 7
x = 3
like nha
e) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\cdot\left(2x-15\right)^2-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\cdot\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left(2x-15\right)^3=0\) hoặc \(\left(2x-15\right)^2-1=0\)
+)TH1: \(\left(2x-15\right)^3=0\)
\(\Rightarrow2x-15=0\)
\(\Rightarrow2x=15\)
\(\Rightarrow x=\frac{15}{2}\)
+)TH2: \(\left(2x-15\right)^2-1=0\)
\(\Rightarrow\left(2x-15\right)^2=1\)
\(\Rightarrow\left[{}\begin{matrix}2x-15=1\\2x-15=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x=16\\2x=14\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)
Vậy \(x=\frac{15}{2}\) hoặc \(x=8\) hoặc \(x=7\)
a) \(2^x-17=15\Rightarrow2^x=32\)
Mà \(2^5=32\Rightarrow x=5\)
Vậy x = 5
b)\(\left(7x-11\right)^3=2^5\cdot5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=1000\)
\(\Rightarrow\left(7x-11\right)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(\Rightarrow7x=21\)
\(\Rightarrow x=3\)
Vậy x = 3
c)\(x^{10}=1^x\Rightarrow x^{10}=1\)(số 1 có luỹ thừa là bao nhiêu thì vẫn là 1 thui)\(\Rightarrow x=1\)
Vậy x = 1
d) \(x^{10}=x\Rightarrow x^{10}-x=0\)
\(\Rightarrow x\left(x^9-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x^9-1=0\)
+)TH1: \(x=0\)
+)TH2: \(x^9-1=0\Rightarrow x^9=1\Rightarrow x=1\)
Vậy x = 0 hoặc x = 1
a: =>15-(x-2)=-13-27=-40
=>x-2=15+40=55
hay x=57
b: =>5-x=-114+12=-102
=>x=107
c: \(\Leftrightarrow\left|x\right|=-1-5=-6\)(vô lý)
d: \(\Leftrightarrow\left|x-3\right|=3\)
=>x-3=3 hoặc x-3=-3
=>x=6 hoặc x=0
a./ \(\Leftrightarrow x^{10}=1\Leftrightarrow x=\pm1\)
b./ \(\Leftrightarrow x^{10}-x=0\Leftrightarrow x\left(x^9-1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^9=1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
c./ \(\Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\Leftrightarrow\left(2x-15\right)^3\left(\left(2x-15\right)^2-1\right)=0\Leftrightarrow\orbr{\begin{cases}2x-15=0\\\left(2x-15\right)^2=1\end{cases}}\)
- 2x - 15 = 0 \(\Leftrightarrow x=\frac{15}{2}\)
- 2x - 15 = 1 \(\Leftrightarrow x=\frac{16}{2}=8\)
- 2x - 15 = -1 \(\Leftrightarrow x=\frac{14}{2}=7\)
(2x - 15)⁵ = (2x - 15)³
(2x - 15)⁵ - (2x - 15)³ = 0
(2x - 15)³.[(2x - 15)² - 1] = 0
(2x - 15)³.[(2x - 15)(2x - 15) - 1] = 0
(2x - 15)³.(4x² - 30x - 30x + 225 - 1) = 0
(2x - 15)³.(4x² - 60x + 225 - 1) = 0
(2x - 15)³.(4x² - 60x + 224) = 0
4.(2x - 15)³.(x² - 15x + 56) = 0
4.(2x - 15)³.(x² - 7x - 8x + 56) = 0
4.(2x - 15)³.[(x² - 7x) - (8x - 56)] = 0
4.(2x - 15)³.[x(x - 7) - 8(x - 7)] = 0
4.(2x - 15)³.(x - 7)(x - 8) = 0
(2x - 15)³ = 0 hoặc x - 7 = 0 hoặc x - 8 = 0
*) (2x - 15)³ = 0
2x - 15 = 0
2x = 15
x = 15/2
*) x - 7 = 0
x = 7
*) x - 8 = 0
x = 8
Vậy x = 7; x = 15/2; x = 8
1 x 99 + 3 x 97+... + 49 x 51 cứu với