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AD
23 tháng 7 2023
\(3^x.3^{x+1}-81=162\\ \Rightarrow3^{x+x+1}=162+81\\\Rightarrow 3^{2x+1}=243\\ \Rightarrow3^{2x+1}=3^5\\ \Rightarrow2x+1=5\\ \Rightarrow2x=4\\ \Rightarrow x=2\left(thoaman\right)\)
AD
23 tháng 7 2023
\(a,3^x.3=243\\ \Rightarrow3^x=243:3\\ \Rightarrow3^x=81\\ \Rightarrow3^x=3^4\\ \Rightarrow x=4\\ b,x^{20}=x\\ \Rightarrow x^{20}-x=0\\ \Rightarrow x\left(x^{19}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x^{19}-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
\(c,2^x.16^2=1024\\ \Rightarrow2^x=1024:16^2\\ \Rightarrow2x=4\\ \Rightarrow x=4:2=2\)
\(d,64.4^x=16^8\\ \Rightarrow2^6.4^x=\left(2^4\right)^8\\\Rightarrow 4^x=2^{32}:2^6\\ \Rightarrow4^x=2^{26}\\ \Rightarrow4^x=\left(2^2\right)^{13}\\ \Rightarrow4^x=4^{13}\\ \Rightarrow x=13\\ e,2^x.4=128\\ \Rightarrow2^x=128:4\\ \Rightarrow2^x=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5\)
@seven
23 tháng 7 2023
a: =>3^x=81
=>x=4
b: =>x(x^19-1)=0
=>x=0 hoặc x=1
c: =>2^x=1024:256=4
=>x=2
d: =>4^x=4^16:4^3=4^13
=>x=13
e: =>2^x=32
=>x=5
AH
Akai Haruma
Giáo viên
23 tháng 7 2023
Lời giải:
$3^{2x+2}=9^{x+3}$
$3^{2x+2}=(3^2)^{x+3}=3^{2(x+3)}=3^{2x+6}$
$\Rightarrow 2x+2=2x+6$
$\Rightarrow 2=6$ (vô lý)
Vậy không có x thỏa mãn đề.
23 tháng 7 2023
`@` `\text {Ans}`
`\downarrow`
`a)`
\(5^x+5^{x+2}=650\)
`\Rightarrow 5^x + 5^x . 5^2 = 650`
`\Rightarrow 5^x . (1 + 5^2) = 650`
`\Rightarrow 5^x . 26 = 650`
`\Rightarrow 5^x = 650 \div 26`
`\Rightarrow 5^x = 25`
`\Rightarrow 5^x = 5^2`
`\Rightarrow x = 2`
Vậy, `x = 2`
`b)`
`(4x + 1)^2 = 25.9`
`\Rightarrow (4x + 1)^2 = 225`
`\Rightarrow (4x + 1)^2 = (+-15^2)`
`\Rightarrow`\(\left[{}\begin{matrix}4x-1=15\\4x-1=-15\end{matrix}\right.\)
`\Rightarrow `\(\left[{}\begin{matrix}4x=16\\4x=-14\end{matrix}\right.\)
`\Rightarrow `\(\left[{}\begin{matrix}x=4\\x=-\dfrac{7}{2}\end{matrix}\right.\)
Vậy, `x \in`\(\left\{-\dfrac{7}{2};4\right\}\)
`c)`
\(2^x+2^{x+3}=144\)
`\Rightarrow 2^x + 2^x . 2^3 = 144`
`\Rightarrow 2^x . (1 + 2^3) = 144`
`\Rightarrow 2^x . 9 = 144`
`\Rightarrow 2^x = 144 \div 9`
`\Rightarrow 2^x = 16`
`\Rightarrow 2^x = 2^4`
`\Rightarrow x = 4`
Vậy, `x = 4`
`d)`
\(3^{2x+2}=9^{x+3}\)
`\Rightarrow `\(3^{2x+2}=\left(3^2\right)^{x+3}\)
`\Rightarrow `\(3^{2x+2}=3^{2x+6}\)
`\Rightarrow 2x + 2 = 2x + 6`
`\Rightarrow 2x - 2x = 6 - 2`
`\Rightarrow 0 = 4 (\text {vô lý})`
Vậy, `x` không có giá trị nào thỏa mãn.
`e)`
\(x^{15}=x^2\)
`\Rightarrow `\(x^{15}-x^2=0\)
`\Rightarrow `\(x^2\cdot\left(x^{13}-1\right)=0\)
`\Rightarrow `\(\left[{}\begin{matrix}x^2=0\\x^{13}-1=0\end{matrix}\right.\)
`\Rightarrow `\(\left[{}\begin{matrix}x=0\\x^{13}=1\end{matrix}\right.\)
`\Rightarrow `\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
Vậy, `x \in`\(\left\{0;1\right\}.\)
AD
23 tháng 7 2023
\(a,5^x+5^{x+2}=650\\ \Rightarrow5^x+5^x.5^2=650\\ \Rightarrow5^x\left(1+5^2\right)=650\\ \Rightarrow5^x.26=650\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)
\(b,\left(4x+1\right)^2=25.9\\\Rightarrow\left(4x+1\right)^2=225\\ \Rightarrow\left[{}\begin{matrix}4x+1=15\\4x+1=-15\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-4\end{matrix}\right.\)
\(c,2^x+2^{x+3}=144\\ \Rightarrow2^x+2^x.2^3=144\\ \Rightarrow2^x\left(1+2^3\right)=144\\ \Rightarrow2^x=144:\left(1+2^3\right)\\ \Rightarrow2^x=16\\ \Rightarrow2^x=2^4\\ \Rightarrow x=4\)
\(d,3^{x+2}=9^{x+3}\\ \Rightarrow3^{x+2}=\left(3^2\right)^{x+3}\\ \Rightarrow3^{x+2}=3^{2x+6}\\ \Rightarrow x+2=2x+6\\ \Rightarrow x-2x=6-2\\ \Rightarrow-x=4\\ \Rightarrow x=-4\)
\(e,x^{15}=x^2\\ \Rightarrow x^{15}-x^2=0\\ \Rightarrow x^2\left(x^{13}-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x^2=0\\x^{13}-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
23 tháng 7 2023
a: =>5^x+5^x*25=650
=>5^x*26=650
=>5^x=25
=>x=2
b: =>4x+1=15 hoặc 4x+1=-15
=>4x=-16 hoặc 4x=14
=>x=7/2 hoặc x=-8
c: =>2^x*9=144
=>2^x=16
=>x=4
d: =>2x+2=2x+6
=>2=6(loại)
e: =>x^2(x^13-1)=0
=>x=0 hoặc x=1
AH
Akai Haruma
Giáo viên
16 tháng 7 2023
Lời giải:
a. $2^3.8=2^3.2^3=2^6$
b. $5^2.25=5^2.5^2=5^4$
c. $27:3^2=3^3:3^2=3^1$
d. $4^2.16=4^2.4^2=4^4$
e. $5^3.5^6=5^9$
f. $3^4.3=3^5$
g.$3^5.4^5=(3.4)^5=12^5$
h. $8^5.2^3=(2^3)^5.2^3=2^{15}.2^3=2^{18}$
i. $a^3.a^5=a^8$
j. $x^7.x.x^4=x^{7+1+4}=x^{12}$
k. $5^6:5^3=5^3$
l. $3^{15}:3^3=3^{15-3}=3^{12}$
m. $4^6:4^6=4^0=1$
n. $9^8:3^2=(3^2)^8:3^2=3^{16}:3^2=3^{14}$
o. $a:a=a^0=1$
p. $5^8.5.5^2=5^{8+1+2}=5^{11}$
q. $4.4^3=4^4$
r. $3.3^4=3^5$
s. $36.6^5=6^2.6^5=6^7$
t. $2^5.2^3=2^8$
u. $3^{10}:3^3=3^7$
v. $2^{10}:2^3=2^7$
w. $5^8:25=5^8:5^2=5^6$
x. $16:2^3=2^4:2^3=2^1$
y. $4.2^3=2^2.2^3=2^5$
z. $2^{10}:4=2^{10}:2^2=2^8$
AD
23 tháng 7 2023
\(f,\left(2x+1\right)^3=343\\\Rightarrow \left(2x+1\right)^3=7^3\\ \Rightarrow2x+1=7\\ \Rightarrow2x=6\\ \Rightarrow x=3\\ g,\left(x-1\right)^3=125\\ \Rightarrow\left(x-1\right)^3=5^3\\ \Rightarrow x-1=5\\ \Rightarrow x=6\\ h,2^{x+2}-2^x=96\\ \Rightarrow2^x.2^2-2^x=96\\ \Rightarrow2^x.\left(2^2-1\right)=96\\ \Rightarrow2^x=96:\left(2^2-1\right)\\ \Rightarrow2^x=32\\ \Rightarrow2^x=2^5\\ \Rightarrow x=5\)
\(i,\left(x-5\right)^4=\left(x-5\right)^6\\ \Rightarrow\left(x-5\right)^4\left(1-\left(x-5\right)^2\right)=0\\\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^4=0\\1-\left(x-5\right)^2=0\end{matrix}\right. \\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\\x-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\left(t/m\right)\\x=6\left(t|m\right)\\x=4\left(loại\right)\end{matrix}\right.\)
\(j,720:\left[41-\left(2x-5\right)\right]=2^3.5\\ \Rightarrow720:\left(41-2x+5\right)=40\\ \Rightarrow\left(46-2x\right)=720:40\\ \Rightarrow46-2x=18\\ \Rightarrow2x=46-18=28\\ \Rightarrow x=28:2=14\)
@seven
23 tháng 7 2023
f: =>2x+1=7
=>2x=6
=>x=3
g: =>x-1=5
=>x=6
h: =>2^x*3=96
=>2^x=32
=>x=5
i: =>(x-5)^4*[(x-5)^2-1]=0
=>(x-5)(x-4)(x-6)=0
=>x=5;x=4;x=6
j: =>41-(2x-5)=720:40=18
=>2x-5=23
=>2x=28
=>x=14
PP
1
NH
23 tháng 7 2023
f)
`(2x+1)^3=343`
`(2x+1)^3=7^3`
`=>2x+1=7`
`2x=7-1`
`2x=6`
`x=6:2`
`x=3`
g)
`(x-1)^3 =125`
`(x-1)^3 =5^3`
`=>x-1=5`
`x=6`
h)
`2^(x+2)-2^x=96`
`2^x *2^2 -2^x =96`
`2^x (2^2 -1)=96`
`2^x *3=96`
`2^x =32`
`2^x =2^5`
`=>x=5`
i)
`(x-5)^4 =(x-5)^6` (`x>=5`)
`(x-5)^6 -(x-5)^4 =0`
`(x-5)^4 [(x-5)^2 -1]=0`
`=>x-5=0` hoặc `(x-5)^2 -1=0`
`<=>x=5` hoặc `(x-5)^2 =1`
`<=>x=5` hoặc `x-5=1` hoặc `x-5=-1`
`<=>x=5` hoặc `x=6` hoặc `x=4`
j)
`720:[41-(2x-5)]=2^3 *5`
`720:[41-(2x-5)]=8*5`
`720:[41-(2x-5)]=40`
`41-(2x-5)=720:40`
`41-(2x-5)=18`
`2x-5=41-18`
`2x-5=23`
`2x=28`
`x=14`
a, 3\(^x\).3 = 243
3\(^x\) = 243: 3
3\(^x\) = 81
3\(^x\) = 34
\(x\) = 4
b, \(x^{20}\) = \(x\)
\(x^{20}\) - \(x\) = 0
\(x\)(\(x^{19}\) - 1) = 0
\(\left[{}\begin{matrix}x=0\\x^{19}=1\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
vậy \(\in\) {0; 1}
c, 2\(^x\).162 = 1024
2\(^x\) = 1024: 162
2\(^x\) = 210: 28
2\(^x\) = 22
\(x\) = 2
d, 64.4\(^x\) = 168
4\(^x\) = 168:64
4\(^x\) = (42)8 : 43
4\(^x\) = 413
\(x\) = 13
e, 2\(^x\).4 = 128
2\(^x\) = 128:4
2\(^x\) = 32
2\(^x\) = 25
\(x\) = 5