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a) ( 3x - 2 )5 = -32
<=> ( 3x - 2 )5 = -25
<=> 3x - 2 = -2
<=> 3x = 0
<=> x = 0
b) ( 3 - 2x )4 = 81
<=> ( 3 - 2x ) = 34
<=> 3 - 2x = 3
<=> 2x = 0
<=> x = 0
c) ( x - 3 )2 = ( 3x + 4 )2
<=> ( x - 3 )2 - ( 3x + 4 )2 = 0
<=> [ x - 3 - ( 3x + 4 ) ][ x - 3 + ( 3x + 4 ] = 0
<=> [ x - 3 - 3x - 4 ][ x - 3 + 3x + 4 ] = 0
<=> [ -2x - 7 ][ 4x + 1 ] = 0
<=> \(\orbr{\begin{cases}-2x-7=0\\4x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{7}{2}\\x=-\frac{1}{4}\end{cases}}\)
d) Mời các cao nhân chứ em tịt rồi ạ :((
a, \(3^{2x+2}=9^{10}\\ 3^{2x+2}=\left(3^2\right)^{10}\\ 3^{2x+2}=3^{20}\\ \Rightarrow2x+2=20\\ \Rightarrow2x=18\\ \Rightarrow x=9\)Vậy x = 9
b, \(3^{3x}=27^{13}\\ 3^{3x}=\left(3^3\right)^{13}\\ 3^{3x}=3^{39}\\ \Rightarrow3x=39\\ \Rightarrow x=13\)Vậy x = 13
c, \(2^x=4^6\cdot16^3\\ 2^x=\left(2^2\right)^6\cdot\left(2^4\right)^3\\ 2^x=2^{12}\cdot2^{12}\\ 2^x=2^{24}\\ \Rightarrow x=24\)Vậy x = 24
d, \(2^x=32^5\cdot64^6\\ 2^x=\left(2^5\right)^5\cdot\left(2^6\right)^6\\ 2^x=2^{25}\cdot2^{36}\\ 2^x=2^{61}\\ \Rightarrow x=61\)Vậy x = 61
32 < 2x < 22x-3 . 28-2x
=> 25 < 2x < 22x - 3 . 28 - 2x
=> 25 < 2x < 25
=> 2x = 25
=> x = 5
a)2x+3+2x=144
2x*23+2x=144
2x * (23+1)=144
2x * 9 =144
2x=144/9=16
2x=16 =>x=4
b) 7x+7x+1=392
7x + 7x * 7 =392
7x * (1+7)=392
7x * 8= 392
7x= 392/8=49
7x=49 => x=2
d) 3x+3x+3=2268
3x+ 3x * 33=2268
3x *(1+33)=2268
3x*28=2268
3x=2268/28
3x=81 =>x=4
e) 9x+2+9x-92*82=0
9x*92+9x-92 *82=0
9x*(92+1)-92*82=0
9x*82-92*82=0
82*(9x-92)=0
=>9x-92=0
9x=0+92=92
=>x=2
f)8x. 16-2x=45
23x. 24 . -2x=45
23x+ 4 . -2x =45
23x-8x=45
2-5x =210
=>-5x=10 =>x=-2
a ) \(\left(2x-1\right)^4=81\)
\(\Leftrightarrow\left(2x-1\right)^4=3^4\)
\(\Leftrightarrow2x-1=3\)
\(\Leftrightarrow x=2\)
Vậy \(x=2.\)
b ) \(\left(x-1\right)^5=-32\)
\(\Leftrightarrow\) \(\left(x-1\right)^5=-2^5\)
\(\Leftrightarrow x-1=-2\)
\(\Leftrightarrow x=-1\)
Vậy \(x=-1.\)
c ) \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Leftrightarrow\left(2x-1\right)^6-\left(2x-1\right)^8=0\)
\(\Leftrightarrow\left(2x-1\right)^6\left[1-\left(2x-1\right)^2\right]=0\)
\(\Leftrightarrow\left(2x-1\right)^6\left[\left(1-2x+1\right)\left(1+2x-1\right)\right]=0\)
\(\Leftrightarrow\left(2x-1\right)^6\left[\left(2-2x\right).2x\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^6=0\\2-2x=0\\2x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\2x=2\\x=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=1\\x=0\end{matrix}\right.\)
Vậy ...............
a) (2x-1)4=81
\(\Leftrightarrow\)\(\left[\begin{array}{} (2x-1)^4=(3)^4\\ (2x-1)^4=(-3)^4 \end{array}\right.\)
\(\Rightarrow\)\(\left[\begin{array}{} 2x-1=3\\ 2x-1=-3 \end{array}\right.\)
\(\Rightarrow\)\(\left[\begin{array}{} 2x=3+1\\ 2x=-3+1 \end{array}\right.\)
\(\Rightarrow\)\(\left[\begin{array}{} 2x=4\\ 2x=-2 \end{array}\right.\)
\(\Rightarrow\)\(\left[\begin{array}{} x=4:2\\ x=-2:2 \end{array}\right.\)
\(\Rightarrow\)\(\left[\begin{array}{} x=2\\ x=-1 \end{array}\right.\)
Vậy x=2 hoặc x=-1
b) (x-1)5= -32
\(\Leftrightarrow\)\( (x-1)^5=(-2)^5 \)
\(\Rightarrow\)\( (x-1)=-2 \)
\(\Rightarrow\)\( x=-2+1 \)
\(\Rightarrow\)\( x=-1 \)
Vậy x=-1
c) ( 2x-1)6= ( 2x-1)8
\(\Leftrightarrow\) (2x-1)6=(2x-1)8.
\(\Leftrightarrow\)(2x-1)8-(2x-1)6=0.
\(\Leftrightarrow\)(2x-1)6)[(2x-1)2-1]=0.
\(\Leftrightarrow\)(2x-1)6(2x-1+1)(2x+1+1)=0.
\(\Leftrightarrow\)(2x-1)62x(2x+2)=0.
\(\Leftrightarrow\)(2x-1)6<=>2x(2x-1)=0.\(\Rightarrow x=\dfrac{1}{2}\)
hoặc 2x=0\(\Rightarrow\)x=0
hoặc 2x+2=0\(\Rightarrow\)2x=-2\(\Leftrightarrow\)x=-2:2\(\Leftrightarrow\)x=-1
Vậy x=\(\dfrac{1}{2}\)hoặc x=0 hoặc x=-1
Chúc bạn học tốt !!!
32/2x - (-2)^5 = (-2)^3
32/2x - (-32)= -8
32/2x +32= -8
32/2x= (-8) - 32
32/2x= -40
2x= -40.32
2x=-1280
x=-1280:2
x=-640
Vậy: x= -640
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