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\(7^{x+2}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}\left(7^3+2\right)=345\)
\(\Leftrightarrow7^{x-1}=1\)
\(\Leftrightarrow x-1=0\Rightarrow x=1\)
\(7^{x+2}+2.7^{x-1}=345\)
⇒ \(7^{x-1}.7^3+2.7^{x-1}=345\)
⇒ \(7^{x-1}.\left(7^3+2\right)=345\)
⇒ \(7^{x-1}.345=345\)
⇒ \(7^{x-1}=345:345\)
⇒ \(7^{x-1}=1\)
⇒ \(7^{x-1}=7^0\)
⇒ \(x-1=0\)
⇒ \(x=0+1\)
⇒ \(x=1\)
Vậy \(x=1.\)
Chúc bạn học tốt!
a) 2x + 2 - 2x = 96
=> 2x . 4 - 2x = 96
=> 2x . (4 - 1) = 96
=> 2x . 3 = 96
=> 2x = 96 : 3
=> 2x = 32
=> 2x = 25
=> x = 5
a) 2x + 2 - 2x = 96
=> 2x. 22 - 2x = 96
=> 2x( 4 - 1 ) = 96
=> 2x = 96 : 3
=> 2x = 25
=> x = 5
\(7^{x+2}+2.7^{x-1}=\frac{345}{7}\Leftrightarrow7^{x+3}+2.7^x=345\Leftrightarrow7^x\left(7^3+2\right)=345\)
\(\Rightarrow7^x345=345\Rightarrow7^x=1\Rightarrow x=0\)
Vậy \(x=0\)
a.\(3^{-2}.3^2.27^x=\frac{1}{3}\)
\(\Rightarrow3^{-2+2}.\left(3^3\right)^x=\frac{1}{3}\)
\(\Rightarrow3^0.3^{3x}=3^{-1}\)
\(\Rightarrow3^{3x}=3^{-1}\)
=> 3x=-1
=> x=\(-\frac{1}{3}\)
b.\(7^{x+2}+2.7^{x-1}=345\)
\(\Rightarrow7^{x-1}.\left(7^3+2\right)=345\)
\(\Rightarrow7^{x-1}.345=345\)
=> 7x-1=345 : 345
=> 7x-1=1
=> 7x-1=70
=> x-1=0
Vậy x=1.
c.\(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Rightarrow\left(2x-1\right)\in\left\{-1;0;1\right\}\)
=> 2x-1=-1 hoặc 2x-1=0 hoặc 2x-1=1
=> 2x=0 hoặc 2x=1 hoặc 2x=2
=> x=0 hoặc x=\(\frac{1}{2}\) hoặc x=1
Vậy \(x\in\left\{0;\frac{1}{2};1\right\}\)
\(\left(\frac{4}{9}\right)^n=\left(\frac{2}{3}\right)^5\)
<=>\(\left(\frac{2}{3}\right)^{\frac{n}{2}}=\left(\frac{2}{3}\right)^5\)
<=>\(\frac{n}{2}=5\)
<=>n=10
\(\left(\frac{4}{9}\right)^n=\left(\frac{2}{3}\right)^5\)
\(\Rightarrow\left(\frac{2}{3}\right)^{2n}=\left(\frac{2}{3}\right)^5\)
\(\Rightarrow2n=5\Rightarrow n=\frac{5}{2}\)
Vậy n = 5/2
b,817-279-913=(34)7-(33)9-(32)13
=328-327-326=326.32-326.3-326=326.(32-3-1)=326.5=322.34.5
=322.405 chia hết cho 405
=>817-279-913 chia hết cho 405
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a) 7x+2 + 2.7x-1 = 345
7x-1 . 73 + 2.7x-1 = 345
7x-1.(343+2) = 345
7x-1. 345=345
=> 7x-1=1
=> 7x-1=70
=> x-1 =0
x=1
b)\(\frac{1}{2}\).2x + 2x+2= 28+25
\(\frac{1}{2}\).2x + 2x . 22 = 288
2x . ( \(\frac{1}{2}\)+ 4)= 288
2x . \(\frac{9}{2}\)=288
=>2x=64
2x= 26
=>x=6
c)2.3x +3x-1 = 7.( 32+2.62)
2.3x-1.31 + 3x-1 = 567
3x-1.(6+1)=567
3x-1.7=567
=>3x-1= 81
3x-1=34
=>x-1=4
x=5
a) \(\left|x\left(x-7\right)\right|=x\)
\(\Rightarrow\orbr{\begin{cases}x\left(x-7\right)=x\\x\left(x-7\right)=-x\end{cases}\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=8\\x=6\end{cases}}}\)
b) \(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow x=2,8\)
\(a.\)\(\left|x.\left(x-7\right)\right|=x\)( Đk: \(x\ge0\))
\(\Leftrightarrow\orbr{\begin{cases}x.\left(x-7\right)=x\\x.\left(x-7\right)=-x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=x:x\\x-7=-x:x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-7=1\\x-7=-1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1+7\\x=-1+7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=8\\x=6\end{cases}}\)
\(b.\)\(\left|x-1,1\right|+\left|x+1,2\right|+\left|x+1,3\right|+\left|x+1,4\right|=5x\)( Đk: \(5x\ge0\Leftrightarrow x\ge0\))
\(\Rightarrow x-1,1+x+1,2+x+1,3+x+1,4=5x\)
\(\Leftrightarrow\left(x+x+x+x\right)+\left(-1,1+1,2+1,3+1,4\right)=5x\)
\(\Leftrightarrow4x+2,8=5x\)
\(\Leftrightarrow2,8=5x-4x\)
\(\Leftrightarrow x=2,8\)
\(c.\)\(7^{x+2}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.7^{x+3}+2.7^{x-1}=345\)
\(\Leftrightarrow7^{x-1}.\left(7^{x+3}+2\right)=345\)
\(......................\)
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7x+2+2.7x-1=345
=>7x-1(73+2)=345
=>7x-1=345:345=1
=>x-1=0
=>x=1
7^x-1 . 7^x+3 + 2. 7^x-1 = 345
7^x-1 .(7^x+3 + 2) =345
7^x-1. (7^x+3 + 2) = 7^x+3 -2
7^x-1 =(7^x+3 - 2) : (7^x+3 +2)
7^x-1 = 0
=> x-1 = 1
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