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10x33(x-2)=(3117+3115):3100
10x33(x-2)=3117:3100+3115:3100
10x33(x-2)=3117-100+3115-100
10x33(x-2)=317+315
10x33(x-2)=129 140 163+14 348 907
10x33(x-2)=143 489 070
33(x-2)=143 489 070:10
33(x-2)=14 348 907
33(x-2)=315
=>3(x-2)=15
x-2=15:3
x-2=5
x=5+2
x=7
\(3^x+3^{x+1}+3^{x+2}=117\)
\(\Rightarrow3^x+3^x\cdot3+3^x\cdot3^2=117\)
\(\Rightarrow3^x+3^x\cdot3+3^x\cdot9=117\)
\(\Rightarrow3^x\cdot\left(1+3+9\right)=117\)
\(\Rightarrow3^x\cdot13=117\)
\(\Rightarrow3^x=\frac{117}{13}\)
\(\Rightarrow3^x=9\)
\(\Rightarrow3^x=3^2\)
\(\Rightarrow x=2\)
a) \(2^{x-1}+2^{x+1}+2^{x+2}=104\)
=> \(2^{x-1}+2^x\cdot2+2^x\cdot2^2=104\)
=> \(2^x:2+2^x\cdot\left(2+2^2\right)=104\)
=> \(2^x\cdot\frac{1}{2}+2^x\cdot6=104\)
=> \(2^x\cdot\left(\frac{1}{2}+6\right)=104\Rightarrow2^x=104:\left(\frac{1}{2}+6\right)=104:\frac{13}{2}=16\)
=> \(x=4\)
b) 123 - 5.(x+4) = 38
=> 5.(x+4) = 123 - 38
=> 5.(x+4) = 85
=> (x+4) = 85 : 5
=> x+4 = 17
=> x = 17 - 4
=> x = 13
c) 2.x - 138 = 23.32
=>2.x - 138 = 736
=>2.x = 736 + 138
=>2.x = 874
=> x = 874 : 2
=> x = 437
d) 70 - 5.(x-3) = 45
=> 5.(x-3) = 70 - 45
=> 5.(x-3) = 25
=> (x-3) = 25 : 5
=> x-3 = 5
=> x = 5 + 3
=> x = 8
3x - 3x - 1 + 3x - 2 = 117
<=> 3x - 2 . (32 + 31 + 1)
<=> 13 . 3x - 2
<=> 3x - 2 = 117 : 13
<=> 3x - 2 = 9
<=> 3x - 2 = 32
<=> x - 2 = 2
<=> x = 2 - 2
<=> x = 2
=> x = 2
3x - 3x - 1 + 3x - 2 = 117
<=> 3x - 2 . (32 + 31 + 1)
<=> 13 . 3x - 2
<=> 3x - 2 = 117 : 13
<=> 3x - 2 = 9
<=> 3x - 2 = 32
<=> x - 2 = 2
<=> x = 2 - 2
<=> x = 2
=> x = 2