a) 210 : x - \(\dfrac{1}{2}\) = 20,5
b) 7.3x + 20.3x = 325
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14 tháng 8 2023
7 . 3x + 20 . 3x = 325
=> 3x ( 7+20) = 325
=> 3x . 27 = 325
=> 325-x = 27 = 33
=> 25 - x = 3
=> x = 25 - 3 = 22
ND
Nguyễn Đức Trí
VIP
14 tháng 8 2023
\(7.3^x+20.3^x=3^{25}\)
\(\Rightarrow3^x\left(7+20\right)=3^{25}\)
\(\Rightarrow3^x.27=3^{25}\)
\(\Rightarrow3^x.3^3=3^{25}\)
\(\Rightarrow3^{x+3}=3^{25}\Rightarrow x+3=25\Rightarrow x=22\)
TT
2
25 tháng 11 2021
\(\dfrac{x+2}{327}+\dfrac{x+3}{326}+\dfrac{x+4}{325}+\dfrac{x+5}{324}+\dfrac{x+349}{5}=0\)
\(\Rightarrow\left(\dfrac{x+2}{327}+1\right)+\left(\dfrac{x+3}{326}+1\right)+\left(\dfrac{x+4}{325}+1\right)+\left(\dfrac{x+5}{324}+1\right)+\left(\dfrac{x+349}{5}-4\right)=0\)
\(\Rightarrow\dfrac{x+329}{327}+\dfrac{x+329}{326}+\dfrac{x+329}{325}+\dfrac{x+329}{324}+\dfrac{x+329}{5}=0\)
\(\Rightarrow\left(x+329\right)\left(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+329=0\\\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}=0\left(vôlí\right)\end{matrix}\right.\)
\(\Rightarrow x=-329\)
MH
25 tháng 11 2021
\(\dfrac{x+2}{327}+\dfrac{x+3}{326}+\dfrac{x+4}{325}+\dfrac{x+5}{324}+\dfrac{x+349}{5}=0\)
⇔ \(\left(\dfrac{x+2}{327}+1\right)+\left(\dfrac{x+3}{326}+1\right)+\left(\dfrac{x+4}{325}+1\right)+\left(\dfrac{x+5}{324}+1\right)+\)
\(\left(\dfrac{x+349}{5}-4\right)=0\)
⇔ \(\dfrac{x+329}{327}+\dfrac{x+329}{326}+\dfrac{x+329}{325}+\dfrac{x+329}{324}+\dfrac{x+329}{5}=0\)
⇔ \(\left(x+329\right)\left(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}\right)=0\)
⇔ \(x+329=0\) Vì \(\left(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}\right)\) ≠ 0
⇔ \(x=-329\)
NN
13 tháng 8 2023
\(\dfrac{x+1}{3}+\dfrac{x+1}{4}+\dfrac{x+1}{5}=\dfrac{x+1}{6}\)
\(\dfrac{x+1}{3}+\dfrac{x+1}{4}+\dfrac{x+1}{5}-\dfrac{x+1}{6}=0\)
\(\left(x+1\right)\left(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}\right)=0\)
\(\)vì \(\dfrac{1}{3}>\dfrac{1}{6};\dfrac{1}{4}>\dfrac{1}{6};\dfrac{1}{5}>\dfrac{1}{6}=>\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}>0\)
\(=>x+1=0\)
\(=>x=-1\)
b,
\(\dfrac{x+1}{2020}+\dfrac{x+2}{2019}=\dfrac{x+3}{2018}+\dfrac{x+4}{2017}\)
\(\left(\dfrac{x+1}{2020}+1\right)+\left(\dfrac{x+2}{2019}+1\right)=\left(\dfrac{x+3}{2018}+1\right)+\left(\dfrac{x+4}{2017}+1\right)\)
\(\dfrac{x+2021}{2020}+\dfrac{x+2021}{2019}=\dfrac{x+2021}{2018}+\dfrac{x+2021}{2017}\)
\(=>\dfrac{x+2021}{2020}+\dfrac{x+2021}{2019}-\dfrac{x+2021}{2018}-\dfrac{x+2021}{2017}=0\)
\(=>\left(x+2021\right)\left(\dfrac{1}{2020}+\dfrac{1}{2019}-\dfrac{1}{2018}-\dfrac{1}{2017}\right)=0\)
Vì \(\dfrac{1}{2020}< \dfrac{1}{2018};\dfrac{1}{2019}< \dfrac{1}{2017}=>\dfrac{1}{2020}+\dfrac{1}{2019}-\dfrac{1}{2018}-\dfrac{1}{2017}< 0\)
\(=>x+2021=0\)
\(=>x=-2021\)
c,
\(\dfrac{x+2}{327}+\dfrac{x+3}{326}+\dfrac{x+4}{325}+\dfrac{x+5}{324}+\dfrac{x+349}{5}=0\)
\(\left(\dfrac{x+2}{327}+1\right)+\left(\dfrac{x+3}{326}+1\right)+\left(\dfrac{x+4}{325}+1\right)+\left(\dfrac{x+5}{324}+1\right)+\left(\dfrac{x+349}{5}-4\right)=0\)
\(\dfrac{x+329}{327}+\dfrac{x+329}{326}+\dfrac{x+329}{325}+\dfrac{x+329}{324}+\dfrac{x+329}{5}=0\)
\(=>\left(x+329\right)\left(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}\right)=0\)
Vì \(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}>0\)
\(=>x+329=0\)
\(=>x=-329\)
H9
HT.Phong (9A5)
CTVHS
20 tháng 8 2023
\(\dfrac{2}{3}\cdot3^{x+1}-7\cdot3^x=-405\)
\(\Rightarrow3^x\cdot\left(\dfrac{2}{3}\cdot3-7\right)=-405\)
\(\Rightarrow3^x\cdot\left(2-7\right)=-405\)
\(\Rightarrow3^x\cdot-5=-405\)
\(\Rightarrow3^x=-405:-5\)
\(\Rightarrow3^x=81\)
\(\Rightarrow3^x=3^4\)
\(\Rightarrow x=4\)
Vậy: \(x=4\)
20 tháng 8 2023
\(\Leftrightarrow3\cdot\dfrac{2}{3}\cdot3^x-7\cdot3^x=-405\)
=>\(-5\cdot3^x=-405\)
=>3^x=81
=>x=4
23 tháng 9 2021
\(7.3^x=189\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\Rightarrow x=3\)
11 tháng 3 2017
\(\left(\dfrac{x+2}{327}+1\right)+\left(\dfrac{x+3}{326}+1\right)+\left(\dfrac{x+4}{325}+1\right)+\left(\dfrac{x+5}{324}\right)+\left(\dfrac{x+349}{5}-4\right)=0\)
\(\dfrac{x+329}{327}+\dfrac{x+329}{326}+\dfrac{x+329}{325}+\dfrac{x+329}{324}+\dfrac{x+329}{5}=0\)
\(\left(x+329\right)\left(\dfrac{1}{327}+\dfrac{1}{326}+\dfrac{1}{325}+\dfrac{1}{324}+\dfrac{1}{5}\right)=0\)
\(\Rightarrow\) x +329 =0 vay x= - 329
DT
14 tháng 4 2022
a) 4/9 x ( 3/5 + 8/5 - 2/10 )
= 4/9 x 1
=4/9
b) ( 312 + 325 - 247 ) : 13
= 390 : 13
= 30
`@` `\text {Ans}`
`\downarrow`
`a)`
`210 \div x - 1/2 = 20,5`
`=> 210 \div x = 20,5 + 1/2`
`=> 210 \div x =21`
`=> x = 210 \div 21`
`=> x = 10`
Vậy, `x = 10.`
`b)`
`7 * 3^x + 20*3^x = 3^25`
`=> 3^x * (7+20) = 3^25`
`=> 3^x * 27 = 3^25`
`=> 3^x * 3^3 = 3^25`
`=> 3^x = 3^25 \div 3^3`
`=> 3^x = 3^22`
`=> x = 22`
Vậy, `x = 22.`
a) \(210:x-\dfrac{1}{2}=20,5\)
\(\Rightarrow210:x=20,5+\dfrac{1}{2}\)
\(\Rightarrow210:x=21\)
\(\Rightarrow x=\dfrac{210}{21}\)
\(\Rightarrow x=10\)
b) \(7\cdot3^x+20\cdot3^x=3^{25}\)
\(\Rightarrow3^x\cdot\left(7+20\right)=3^{25}\)
\(\Rightarrow3^x\cdot27=3^{25}\)
\(\Rightarrow3^x\cdot3^3=3^{25}\)
\(\Rightarrow3^{x+3}=3^{25}\)
\(\Rightarrow x+3=25\)
\(\Rightarrow x=25-3\)
\(\Rightarrow x=22\)