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<=> (32+1 ).33(x-2) =317+315
<=> (32+1 ).33(x-2) =315.(32+1)
<=> 33(x-2) = 315
<=> 3(x-2) = 15
<=> x-2 = 5
<=> x= 7
\(10.3^{3.\left(x-2\right)}=\left(3^{117}+3^{115}\right):3^{100}\)
\(10.3^{3x-9}=3^{117}:3^{100}+3^{115}:3^{100}\)
\(10.3^{3x}:3^9=3^{17}+3^{15}\)
\(10.9^x:19683=143489070\)
...................................................
3x-2-19=62
=> 3x-2=62+19
=> 3x-2=81
=> 3x-2=34
=> x-2=4
=> x=4+2
=> x=6
10.3x=3117+3115
=> 10.3x=3115.(32+1)
=> 10.3x=3115.(9+1)
=> 3x.10=3115.10
=> 3x=3115
=> x=115
2448-(5x+48)=2000
=> 5x+48=2448-2000
=> 5x+48=448
=> 5x=448-48
=> 5x=400
=> x=400:5
=> x=80
1)\(3^{x-2}=62+19=81=3^4\)
=> x- 2 = 4
=> x = 6
2) \(2448-\left(5x+48\right)=2000\)
5x + 48 = 448
5x = 448 - 48
5x = 400
x = 80
3) \(10.3^x=3^{115}\left(3^2+1\right)=3^{115}.10\)
=> x =115
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
Lời giải:
$10.3^x=3^{117}+3^{115}=3^{115}(3^2+1)=10.3^{115}$
$\Rightarrow 3^x=3^{115}$
$\Rightarrow x=115$