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\(3^x\left(1+3\right)=108\\ 3^x\cdot4=108\\ 3^x=27\\ x=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
5.9x + 4.32x + 1 = 1377
=> 5.32x + 4 . 32x.3 = 1377
=> 5 .32x + 12.32x = 1377
=> (5 + 12).32x = 1377
=> 17.32x = 1377
=> 32x = 1377: 17
=> 32x = 81
=> 32x = 34
=> 2x = 4
=> x = 4 : 2
=> x = 2
Vậy ...
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a: Số số hạng từ 0 đến 2012 là: 2012-0+1=2013(số)
Tổng là \(\dfrac{2012\cdot2013}{2}=2025078\)
Theo đề, ta có: 2013x+2025078=2033130
=>2013x=8052
hay x=4
b: \(\Leftrightarrow5\cdot3^{2x}+4\cdot3^{2x}\cdot3=1377\)
\(\Leftrightarrow3^{2x}\cdot17=1377\)
=>32x=81
=>x=2
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a) \(4^{x+2}+4^x=68\)
\(\Rightarrow4^x\cdot\left(4^2+1\right)=68\)
\(\Rightarrow4^x\cdot17=68\)
\(\Rightarrow4^x=\dfrac{68}{17}\)
\(\Rightarrow4^x=4\)
\(\Rightarrow4^x=4^1\)
\(\Rightarrow x=1\)
b) \(5\cdot2^{x+4}-3\cdot2^x=308\)
\(\Rightarrow2^x\cdot\left(5\cdot2^4-3\right)=308\)
\(\Rightarrow2^x\cdot\left(5\cdot16-3\right)=308\)
\(\Rightarrow2^x\cdot77=308\)
\(\Rightarrow2^x=\dfrac{308}{77}\)
\(\Rightarrow2^x=4\)
\(\Rightarrow2^x=2^2\)
\(\Rightarrow x=2\)
c) \(4\cdot3^{x+1}+7\cdot3^x=513\)
\(\Rightarrow3^x\cdot\left(4\cdot3+7\right)=513\)
\(\Rightarrow3^x\cdot19=513\)
\(\Rightarrow3^x=\dfrac{513}{19}\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\)
\(\Rightarrow x=3\)
d) \(5^{x+4}-5^x=3120\)
\(\Rightarrow5^x\cdot\left(5^4-1\right)=3120\)
\(\Rightarrow5^x\cdot\left(625-1\right)=3120\)
\(\Rightarrow5^x\cdot624=3120\)
\(\Rightarrow5^x\cdot\dfrac{3120}{624}\)
\(\Rightarrow5^x=5\)
\(\Rightarrow5^x=5^1\)
\(\Rightarrow x=1\)
f) \(3\cdot4^{2x+1}-16^x=2816\)
\(\Rightarrow3\cdot4^{2x+1}-\left(4^2\right)^x=2816\)
\(\Rightarrow3\cdot4^{2x+1}-4^{2x}=2816\)
\(\Rightarrow4^{2x}\cdot\left(3\cdot4-1\right)=2816\)
\(\Rightarrow4^{2x}\cdot11=2816\)
\(\Rightarrow4^{2x}=\dfrac{2816}{11}\)
\(\Rightarrow4^{2x}=256\)
\(\Rightarrow\left(2^2\right)^{2x}=2^8\)
\(\Rightarrow2^{4x}=2^8\)
\(\Rightarrow4x=8\)
\(\Rightarrow x=2\)
Bài 2:
\(2^x+124=5^y\)
\(\Rightarrow5^y-2^x=124\)
\(\Rightarrow5^y-2^x=125-1\)
\(\Rightarrow\left\{{}\begin{matrix}5^y=125\\2^x=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}5^y=5^3\\2^x=2^0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}y=3\\x=0\end{matrix}\right.\)
Vậy: ....
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Đây chỉ là ý kiến đóng góp thôi nha
1440 : [ 41 - ( 2x-5 ) ] = 2^4.3
1440 : [ 41 - ( 2x-5 ) ] = 16.3
1440 : [ 41 - ( 2x-5 ) ] = 48
[ 41 - ( 2x-5 ) ] = 1440 : 48
[ 41 - ( 2x-5 ) ] = 30
2x-5 = 41-30
2x-5 = 11
2x = 11+5
2x = 16
x = 16:2
x = 8
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3\left(4-x\right)-5\left(2-2x\right)=4.3^2-16.2^2\)
\(12-3x-10+10x=2^2.3^2-2^4.2^2\)
\(2+7x=-28\)
\(7x=-30\)
\(x=\frac{-30}{7}\)
4.32x+1 = 108
<=> 32x.3 = 27
<=> 32x = 9
<=> 32x = 32
<=> 2x = 2
<=> x = 1
\(4.3^{2x+1}=108\)
\(\Leftrightarrow3^{2x+1}=108:4\)
\(\Leftrightarrow3^{2x+1}=27\)
\(\Leftrightarrow3^{2x}.3=27\)
\(\Leftrightarrow3^{2x}=27:3\)
\(\Leftrightarrow3^{2x}=9\)
\(\Leftrightarrow3^{2x}=3^2\)
\(\Leftrightarrow2x=2\)
\(\Leftrightarrow x=2:2\)
\(\Leftrightarrow x=1\)
~ Rất vui vì giúp đc bn ~