2^x+2^x+1+2^x+2=7.4
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17 tháng 8 2015
1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)
2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)
\(2^x=2.2^8=2^9;x=9\)
4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)
\(\Leftrightarrow3^5.x=3^5.5;x=5\)
HK
0
TN
15 tháng 8 2018
\(16^x+7.4^x+5=3.2^x+2\)
<=> \(8.2^x+7.2.2^x+5=3.2^x+2\)
<=> \(8.2^x+7.2.2^x+5-3.2^x-2=0\)
<=> \(2^x\left(8+7.2-3\right)-3=0\)
<=> \(2^x.19=3\)
<=> \(2^x=\frac{3}{19}\)
2 tháng 8 2023
1: =>3^x=81
=>x=4
2: =>2^x=8
=>x=3
3: =>x^3=2^3
=>x=2
4: =>x^20-x=0
=>x(x^19-1)=0
=>x=0 hoặc x=1
5: =>2^x=32
=>x=5
6: =>(2x+1)^3=9^3
=>2x+1=9
=>2x=8
=>x=4
7: =>x^3=115
=>\(x=\sqrt[3]{115}\)
8: =>(2x-15)^5-(2x-15)^3=0
=>(2x-15)^3*[(2x-15)^2-1]=0
=>2x-15=0 hoặc (2x-15)^2-1=0
=>2x-15=0 hoặc 2x-15=1 hoặc 2x-15=-1
=>x=15/2 hoặc x=8 hoặc x=7
VN
Võ Ngọc Phương
VIP
2 tháng 8 2023
1. Tìm số tự nhiên x biết:
1) \(3^x.3=243\)
\(3^x=243:3\)
\(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
_____
2) \(7.2^x=56\)
\(2^x=56:7\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
_____
3) \(x^3=8\)
\(x^3=2^3\)
\(\Rightarrow x=3\)
_____
4) \(x^{20}=x\)
\(x^{20}-x=0\)
\(x\left(x^{19}-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x=1\)
5) \(2^x-15=17\)
\(2^x=17+15\)
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
_____
6) \(\left(2x+1\right)^3=9.81\)
\(\left(2x+1\right)^3=729=9^3\)
\(\rightarrow2x+1=9\)
\(2x=9-1\)
\(2x=8\)
\(x=8:2\)
\(\Rightarrow x=4\)
_____
7) \(x^6:x^3=125\)
\(x^3=125\)
\(x^3=5^3\)
\(\Rightarrow x=5\)
_____
8) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=7\\x=8\end{matrix}\right.\)
_____
9) \(3^{x+2}-5.3^x=36\)
\(3^x.\left(3^2-5\right)=36\)
\(3^x.\left(9-5\right)=36\)
\(3^x.4=36\)
\(3^x=36:4\)
\(3^x=9\)
\(3^x=3^2\)
\(\Rightarrow x=2\)
_____
10) \(7.4^{x-1}+4^{x+1}=23\)
\(\rightarrow7.4^{x-1}+4^{x-1}.4^2=23\)
\(4^{x-1}.\left(7+4^2\right)=23\)
\(4^{x-1}.\left(7+16\right)=23\)
\(4^{x-1}.23=23\)
\(4^{x-1}=23:23\)
\(4^{x-1}=1\)
\(4^{x-1}=4^1\)
\(\rightarrow x-1=0\)
\(x=0+1\)
\(\Rightarrow x=1\)
Chúc bạn học tốt
DD
1
9 tháng 4 2020
a/\(\Leftrightarrow\left(2^4\right)^x+7.\left(2^x\right)^2+5=3.2^x.4\)
Đặt \(2^x=y\) PT trở thành:
\(y^4+7y^2+5=12y\)
\(\Leftrightarrow y^4+7y^2-12y+5=0\)
Giải típ
DD
0
KL
2
H9
HT.Phong (9A5)
CTVHS
27 tháng 9 2023
\(7\cdot4^x=112\)
\(\Rightarrow4^x=\dfrac{112}{7}\)
\(\Rightarrow4^x=16\)
\(\Rightarrow4^x=4^2\)
\(\Rightarrow x=2\)
_____
\(2\cdot5^{x-3}=250\)
\(\Rightarrow5^{x-3}=\dfrac{250}{2}\)
\(\Rightarrow5^{x-3}=125\)
\(\Rightarrow5^{x-3}=5^3\)
\(\Rightarrow x-3=3\)
\(\Rightarrow x=3+3\)
\(\Rightarrow x=6\)
____
\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)
\(=12:\left\{400:\left[500-\left(125+25\cdot7\right)\right]\right\}+10\)
\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)
\(=12:\left[400:\left(500-300\right)\right]+10\)
\(=12:\left(400:200\right)+10\)
\(=12:2+10\)
\(=6+10\)
\(=16\)
T
27 tháng 9 2023
\(7\cdot4^x=112\)
\(\Rightarrow4^x=112:7\)
\(\Rightarrow4^x=16\)
\(\Rightarrow4^x=4^2\)
\(\Rightarrow x=2\)
Vậy \(x=2.\)
\(---\)
\(2\cdot5^{x-3}=250\)
\(\Rightarrow5^{x-3}=250:2\)
\(\Rightarrow5^{x-3}=125\)
\(\Rightarrow5^{x-3}=5^3\)
\(\Rightarrow x-3=3\)
\(\Rightarrow x=3+3\)
\(\Rightarrow x=6\)
Vậy \(x=6.\)
\(---\)
\(12:\left\{400:\left[500-\left(5^3+5^2\cdot7\right)\right]\right\}+10\)
\(=12:\left\{400:\left[500-\left(125+175\right)\right]\right\}+10\)
\(=12:\left\{400:\left[500-300\right]\right\}+10\)
\(=12:\left\{400:200\right\}+10\)
\(=12:2+10\)
\(=6+10\)
\(=16\)
#\(Toru\)