tìm x ( 2x-6)mũ 100=(2x-6)mũ 200
giải hộ mk nha
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a. \(12^2.3^2.2^3=2^4.3^2.3^2.2^3=2^7.3^4\)
b. \(8^3.3^2.6^3=2^9.3^2.2^3.3^3=2^{12}.3^5\)
c. \(5^{32}.5^2=5^{34}\)
d. \(100^6.2^3=\left(2^2.5^2\right)^6.2^3=2^8.5^8.2^3=2^{11}.5^8\)
e. \(100^2:10^2:5^2=\left(10.5.2\right)^2:10^2:5^2=2^2\)
f. \(121^3-11^2=11^6-11^2=11^2\left(11^4-1\right)\)
(2x - 1)6 = (2x - 1)4
=> (2x - 1)6 - (2x - 1)4 = 0
=> (2x - 1)4.[(2x - 1)2 - 1] = 0
=> \(\orbr{\begin{cases}\left(2x-1\right)^4=0\\\left(2x-1\right)^2-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}2x-1=0\\\left(2x-1\right)^2=1\end{cases}}\Rightarrow\orbr{\begin{cases}2x-1=0\\2x-1=\pm1\end{cases}}\)
Khi 2x - 1 = 0 => x = 1/2
Khi 2x - 1 = -1 => x = 0
Khi 2x - 1 = 1 => x = 1
Vậy \(x\in\left\{\frac{1}{2};0;1\right\}\)là giá trị cần tìm
( 2x - 1 )6 = ( 2x - 1 )4
<=> ( 2x - 1 )6 - ( 2x - 1 )4 = 0
<=> ( 2x - 1 )4[ ( 2x - 1 )2 - 1 ] = 0
<=> \(\orbr{\begin{cases}\left(2x-1\right)^4=0\\\left(2x-1\right)^2-1=0\end{cases}}\)
<=> \(\hept{\begin{cases}x=\frac{1}{2}\\x=1\\x=0\end{cases}}\)( thay = dấu hoặc hộ nhé )
a) \(\left(2x-5\right)^2-\left(2x+3\right)\left(2x-3\right)=10\Leftrightarrow\left(4x^2-20x+25\right)-\left(4x^2-9\right)-10=0\)
\(\Leftrightarrow-20x+24=0\Leftrightarrow x=\frac{6}{5}\)
b) \(\left(4x-1\right)\left(x+2\right)-\left(2x+3\right)^2-5\left(x-1\right)=9\Leftrightarrow-10x-15=0\)
\(\Leftrightarrow x=\frac{-3}{2}\)
c) \(\left(x+1\right)^3-\left(x-1\right)^3-2=6\Leftrightarrow\left(x^3+3x^2+3x+1\right)-\left(x^3-3x^2+3x-1\right)-8=0\)
\(\Leftrightarrow6x^2-6=0\Leftrightarrow x=\pm1\)
d) \(\left(x+2\right)\left(x^2-2x+4\right)-\left(x+1\right)\left(x^2-x+1\right)-3\left(-x-2\right)=5\)
\(\Leftrightarrow\left(x^3+8\right)-\left(x^3+1\right)+3x+6=5\Leftrightarrow3x+8=0\Leftrightarrow x=\frac{-8}{3}\)
Ta có:
a) \(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(5.3^2\right)^{10}.5^{20}}{\left(5^2.3\right)^{15}}=\frac{5^{10}.3^{20}.5^{20}}{5^{30}.3^{15}}=\frac{5^{30}.3^{20}}{5^{30}.3^{15}}=3^5=243\)
b) \(\frac{\left(0,8\right)^5}{\left(0,4\right)^6}=\frac{\left(0,2.2^2\right)^5}{\left(0,2.2\right)^6}=\frac{\left(0,2\right)^5.2^{10}}{\left(0,2\right)^6.2^6}=\frac{2^4}{0,2}=\frac{16}{0,2}=80\)
c) \(\frac{2^{15}.9^4}{6^6.8^3}=\frac{2^{15}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^3}=\frac{2^{15}.3^8}{2^6.3^6.2^9}=\frac{2^{15}.3^8}{2^{15}.3^6}=3^2=9\)
a) \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)
b) \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)
c) \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)
d) \(x^2=x^3\Rightarrow x^3-x^2=0\Rightarrow x^2\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
e) \(3^{x-1}=27\Rightarrow3^{x-1}=3^3\Rightarrow x-1=3\Rightarrow x=4\)
f) \(3^{x+1}=9\Rightarrow3^{x+1}=3^2\Rightarrow x+1=2\Rightarrow x=1\)
g) \(6^{x+1}=36\Rightarrow6^{x+1}=6^2\Rightarrow x+1=2\Rightarrow x=1\)
h) \(3^{2x+1}=27\Rightarrow3^{2x+1}=3^3\Rightarrow2x+1=3\Rightarrow2x=2\Rightarrow x=1\)
i) \(x^{50}=x\Rightarrow x^{50}-x=0\Rightarrow x\left(x^{49}-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1=1^{49}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
4n = 4096
4n = 212
n = 12
5n = 15625
5n = 56
n = 6
6n+3 = 216
6n+3 = 23.33
6n+3 = 63
n + 3 = 3
(1)
(x+1)(x-7)+17>0
<=>x^2-6x+9+1>0
<=>(x-3)^2+1>0(dpcm)
..
(7)
-y^2+4y-4-|x+1|≤0
<=>-(y-2)^2-|x+1|≤0
sum 2 so khong duong ko the la so (+)=>dpcm
2x - 6 nhất định phải bằng 0 hoặc 1 vì nếu cơ số bằng 0 hoặc 1 thì mũ có lớn mấy cũng chỉ bằng 0 hoặc 1.
Ta có 2x - 6 = 1 hoặc 0
Ta thử từng trường hợp
Nếu 2x - 6 = 0 thì 2x = 0 + 6
2x = 6
x = 6 : 2
x = 3 (Chọn)
Nếu 2x - 6 = 1 thì 2x = 6 + 1
2x = 7
x = 7 : 2 (Loại)
Vì 7 ko chia hết cho 2.
Vậy x = 3
(2x-6)100=(2x-6)200
2x-6=1 hoặc 2x-6=0 hoặc 2x-6=-1
2x=7 hoặc 2x=6 hoặc 2x=5
x=7/2 hoặc x=3 hoạc x=5/2