2 mũ x + mũ 3 + 2 mũ x = 144
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a) \(2^x+2^{x+3}=144\)
\(2^x\left(1+2^3\right)=144\)
\(2^x.9=144\)
\(2^x=144:9=16\)
=> \(2^x=2^4\Rightarrow x=4\)
b) \(2^{x-1}+5.2^{x-2}=224\)
\(2^{x-2}\left(2+5\right)=224\)
\(2^{x-2}.7=224\Rightarrow2^{x-2}=32\Rightarrow2^{x-2}=2^5\)
=> x - 2 = 5 => x = 7
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(x - 5)2 = 16
=> (x - 5)2 = 42
=> \(\orbr{\begin{cases}x-5=4\\x-5=-4\end{cases}}\)
=> \(\orbr{\begin{cases}x=9\\x=1\end{cases}}\)
(2x - 1)3 = -64
=> (2x - 1)3 = -43
=> 2x - 1 = -4
=> 2x = -4 + 1
=> 2x = -3
=> x = -3/2
( x - 5)2 = 16
=> (x - 5)2 = 42
=> \(\orbr{\begin{cases}x-5=4\\x-5=-4\end{cases}}\)
=> \(\orbr{\begin{cases}x=9\\x=1\end{cases}}\)
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3^( x-1) = 1/243
=> 3^x : 3 = 1/243
=>3^x = 3/243 = 1/81
=> x = -4 ( vì 3^-4 = 1/(3^4) = 1/81)
2^x + 2^(x + 3) = 144
=> 2^x + 2^x.2^3 = 144
=> 2^x ( 1 + 2^3) = 144
=> 2^x . 9 = 144
=> 2^x = 144/9 = 16
=> x = 4 ( vì 2^4 = 16 )
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a) \(2^{4x}-3^{2x}=144-164:41\)
\(\Leftrightarrow16^x-9^x=144-4\)
\(\Leftrightarrow\) ......
bjan tự tính tiếp đc òi
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b: Ta có: \(2^{x+3}+2^x=144\)
\(\Leftrightarrow2^x\cdot9=144\)
\(\Leftrightarrow2^x=16\)
hay x=4
![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^{x+2}=243\)
\(3^{x+2}=3^5\)
=> x + 2 = 5
=> x = 3
\(2^{x+3}+2^x=144\)
\(2^x.8+2^x=144\)
\(2^x.\left(8+1\right)=144\)
\(2^x.9=144\)
\(2^x=16\)
=> x = 4
\(3^5+2=243\) cái này bạn sai nhé. không ra đâu
\(2^4+3+2^7=147\)cái này bạn sai nhé. không ra đâu
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^x+2^{x+3}=144\)
\(\Rightarrow2^x+2^x.2^3=144\)
\(\Rightarrow2^x.\left(1+2^3\right)=144\)
\(\Rightarrow2^x.9=144\)
\(\Rightarrow2^x=144:9\)
\(\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\)
\(\Rightarrow x=4\)
Vậy x = 4
_Chúc bạn học tốt_
\(2^x+2^{x+3}=144\)
\(\Leftrightarrow2^x+2^x\cdot2^3=144\)
\(\Leftrightarrow2^x+2^x\cdot8=144\)
\(\Leftrightarrow2^x\left(1+8\right)=144\)
\(\Leftrightarrow2^x\cdot9=144\)
\(\Leftrightarrow2^x=144:9\)
\(\Leftrightarrow2^x=16\)
\(\Leftrightarrow2^x=2^4\)
\(\Leftrightarrow x=4\)
Vậy x=4
![](https://rs.olm.vn/images/avt/0.png?1311)
\(4^2.x+2^4.x+3=144\\ \Rightarrow16x+16x+3=144\\ \Rightarrow32x=144-3\\ \Rightarrow32x=141\\ \Rightarrow x=\dfrac{141}{32}\)
2x + 2x + 3 = 144
=> 2x . 1 + 2x . 23 = 144
=> 2x . (1 + 23) = 144
=> 2x . 9 = 144
=> 2x = 144 : 9 = 16
=> x = 4
Ta có:
\(2^{x+3}+2^x=144\Rightarrow2^x.2^3+2^x=144\)
\(\Rightarrow2^x.\left(2^3+1\right)=144\Rightarrow2^x.9=144\)
\(\Rightarrow2^x=144:9\Rightarrow2^x=16\)
\(\Rightarrow2^x=2^4\Rightarrow x=4\)
2x+3 + 2x = 144
2x( 23 +1) = 144
2x . 9 = 144
2x = 16
2x = 24 => x=4