1, 2. 3x+2+4.3x+1=10 . 36
2, 4.3x-2+2.3x+1=4.36+2 .30
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Ta có: \(4.3^{x+2}-2.3^{x+1}=810\)
\(4.3^{x+1}.3-2.3^{x+1}=810\)
\(2.3^{x+1}\left(2.3-1\right)=810\)
\(2.3^{x+1}.5=810\)
\(3^{x+1}=81=3^4\)
x+1=4
x=3
a: =>\(4\cdot3^x\cdot\dfrac{1}{3}+2\cdot3^x\cdot9=4\cdot3^6+2\cdot3^9\)
=>3^x(4*1/3+2*9)=3^6(4+2*3^3)
=>3^x*58/3=3^6*58
=>3^x/3^6=3
=>x-6=1
=>x=7
b: =>\(2^x\cdot\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)=2^7\left(\dfrac{1}{5}+\dfrac{1}{3}\cdot2\right)\)
=>2^x=2^7
=>x=7
\(3^{x+2}+4\cdot3^{x+1}=7\cdot3^6\\ 3^x\cdot3^2+4\cdot3^x\cdot3=5103\\ 3^x\left(9+12\right)=5103\\ 3^x\cdot21=5103\\ 3^x=243\\ 3^x=3^5\\ x=5\)
\(4\cdot3^{x+2}-3^{x-1}=963\\ \Leftrightarrow36\cdot3^x-\dfrac{1}{3}\cdot3^x=963\\ \Leftrightarrow3^x=27\\ \Leftrightarrow x=3\)
\(\left(4.3x-4\right)-2=18\)
\(\Rightarrow12x-4-2=18\)
\(\Rightarrow12x=24\Leftrightarrow x=2\)
a ) 9 . 3x = 81
3x = 9
x = 3
b ) 2x : 4 = 1
2x = 4
x = 2
c ) 2x - 64 = 2
2x = 66
x = 33
d ) 2x = 16
x = 8
e ) 3 ^ 2 . 3 ^ 4 . 3x = 3 ^ 10
3 ^ ( 2 + 4 + x ) = 3 ^ 10
=> 2 + 4 + x = 10
x = 4
f ) 2x + 4 . 2x = 5 . 2 ^ 5
2x + 8 x = 160
10x = 160
x = 16