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\(a,5^x+5^{x+2}=650\\ \Rightarrow a,5^x+5^x.25=650\\ \Rightarrow26.5^x=650\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)
\(b,3^{x.1}+5.3^{x.1}=162\\ \Rightarrow3^x+5.3^x=162\\ \Rightarrow6.3^x=162\\ \Rightarrow3^x=27\\ \Rightarrow3^x=3^3\\ \Rightarrow x=3\)
2x+ 3= x+ 2
2x- x= 2- 3
x= -1
vậy x=-1
b) \(3^{x-1}+5.3^{x-1}=162
\)
\(3^{x-1}.\left(1+5\right)=162\)
\(3^{x-1}.6=162\)
\(3^{x-1}=162:6\)\(\Rightarrow3^{x-1}=27\)
\(3^{x-1}=3^3\)
\(\Rightarrow x-1=3\)
\(\Rightarrow x=4\)
(3x+1)^3=-216=(-6)^3
=>3x+1=-6
=>x=...
3^x-1+5.3^x-1=162
=>3^x-1.(1+5)=162
=>3^x-1.6=162
=>3^x-1=162:6=27
=>3^x-1=3^3
=>x-1=3
=>x=4
Mk sẽ giải từng câu
\(a)\) \(\left(3x+1\right)\left(x-2\right)>0\)
Trường hợp 1 :
\(\hept{\begin{cases}3x+1>0\\x-2>0\end{cases}\Leftrightarrow\hept{\begin{cases}3x>-1\\x>2\end{cases}\Leftrightarrow}\hept{\begin{cases}x>\frac{-1}{3}\\x>2\end{cases}}}\)
\(\Rightarrow\)\(x>2\)
Trường hợp 2 :
\(\hept{\begin{cases}3x+1< 0\\x-2< 0\end{cases}\Leftrightarrow\hept{\begin{cases}3x< -1\\x< 2\end{cases}\Leftrightarrow}\hept{\begin{cases}x< \frac{-1}{3}\\x< 2\end{cases}}}\)
\(\Rightarrow\)\(x< \frac{-1}{3}\)
Vậy \(x>2\) hoặc \(x< \frac{-1}{3}\) thì \(\left(3x+1\right)\left(x-2\right)>0\)
Chúc bạn học tốt ~
a) (3x+1).(x-2)>0
TH1: 3x+1>0 TH2: x-2>0
3x > -1 x>2
x>-1/3
Vậy x>2
\(\Leftrightarrow3^{x-1}\left(1+5\right)=162\)
\(\Leftrightarrow3^{x-1}.6=162\)
\(\Leftrightarrow3^{x-1}=27\)
\(\Leftrightarrow x-1=3\)
\(\Leftrightarrow x=3+1=4\)
\(3^{x-1}+5.3^{x-1}=162\)
\(3^{x-1}.\left(1+5\right)=162\)
\(3^{x-1}.6=162\)
\(3^{x-1}=27\)
\(3^{x-1}=3^3\)
\(\Leftrightarrow x-1=3\)
\(x=4\)
Vậy x = 4
5X+5X+2=650
=>5X.1+5X.52=650
=>5X.(1+52)=650
=>5X.26=650
=>5x=650:26
=>5X=25
=>5X=52
=>X=2
3X-1+5.3X-1=162
=>3X-1.1+5.3X-1=162
=>3X-1.(1+5)=162
=>3X-1.6=162
=>3X-1=162:6
=>3X-1=27
=>3X-1=33
=>3X=33+1
=>3X=34
=>X=4
\(5^x+5^{x+2}=650\Leftrightarrow5^x+5^x.5^2=650\)
\(5^x=650:26=25\Leftrightarrow x=2\)
a) 5X+5X+2=650
=>5X.1+5X.52=650
=>5X.(1+52)=650
=>5X.26=650
=>5x=650:26
=>5X=25
=>5X=52
=>X=2
b) 3X-1+5.3X-1=162
=>3X-1.1+5.3X-1=162
=>3X-1.(1+5)=162
=>3X-1.6=162
=>3X-1=162:6
=>3X-1=27
=>3X-1=33
=>3X=33+1
=>3X=34
=>X=4
=> \(5^x+5^x.5^2=650\)
\(5^x\left(1+5^2\right)=650\Leftrightarrow5^x.26=650\)
\(\Leftrightarrow5^x=25;x=2\)
a) \(5^x+5^{x+2}=650\)
\(5^x+5^x.5^2=650\)
\(5^x.\left(1+5^2\right)=650\)
\(5^x.26=650\)
\(5^x=25\)
\(5^x=5^2\)
\(\Rightarrow x=2\)
Vậy x = 2
b) \(3^{x-1}+5.3^{x-1}=162\)
\(3^{x-1}.\left(1+5\right)=162\)
\(3^{x-1}.6=162\)
\(3^{x-1}=162:6\)
\(3^{x-1}=27\)
\(3^{x-1}=3^3\)
\(\Rightarrow x-1=3\)
\(x=3+1\)
\(x=4\)
Vậy x = 4
a) 5x+5x + 2 = 650
=> 5x+ 5x.52 = 650
=> 5x(1+ 52) = 650
=> 5x.26 = 650
=> 5x = 650:26
=> 5x = 25
=> 5x = 52
=> x = 2
Vậy x = 2
b) 3x-1 + 5.3x-1 = 162
=> 3x-1(1+5) = 162
=> 3x-1. 6 = 162
=> 3x-1 = 162
=> x ko có giá trị
Vậy x ko tìm đc giá trị thỏa mãn đề bài.
1.3\(x-1\) + 5.3\(x-1\) = 162
3\(^{x-1}\).(1 + 5) = 162
3\(x-1\).6 = 162
3\(x-1\) = 162 : 6
3\(^{x-1}\) = 27
3\(^{x-1}\) = 33
\(x-1\) = 3
\(x\) = 3 + 1
\(x\) = 4
Vậy \(x=4\)