a: \(35=5\cdot7;105=3\cdot5\cdot7\)

=>\(ƯCLN\left(35;105\right)=5\cdot7=35\)

\(35⋮x;105⋮x\)

=>\(x\inƯC\left(105;35\right)\)

=>\(x\inƯ\left(35\right)\)

=>\(x\in\left\{1;5;7;35\right\}\)

mà x>5

nên \(x\in\left\{7;35\right\}\)

b: \(144=2^4\cdot3^2;192=2^6\cdot3;240=2^4\cdot3\cdot5\)

=>\(ƯCLN\left(144;192;240\right)=2^4\cdot3=48\)

\(144⋮x;192⋮x;240⋮x\)

=>\(x\inƯC\left(192;144;240\right)\)

=>\(x\inƯ\left(48\right)\)

=>\(x\in\left\{1;2;3;4;6;8;12;16;24;48\right\}\)

mà 10<=x<=99

nên \(x\in\left\{12;16;24;48\right\}\)

Ta có: 2x + 2x + 3 = 144

=> 2x + 2x.23 = 144

=> 2x.(1 + 8) = 144

=> 2x.9 = 144

=> 2x = 144 : 9 = 16 = 24

=> x = 4.

Vậy x= 4

x= 4

a: =>13x-144=25

=>13x=169

hay x=13

Ta tìm được xϵ{3; 4; 6; 12}.

 2^x + 2^{x +3} = 144

=> 2^x (1 + 2³) = 144

=> 2^x . 9 = 144

=> 2^x = 16

=> 2^x = 2⁴

=> x = 4

\(\Rightarrow8\times2^x+2^x=144\)

\(\Rightarrow9\times2^x=144\)

\(\Rightarrow2^x=144\div9=16=2^4\)

Vậy x=4

Bài 2

 x chia hết cho 12; 21; 28 => x ∈ BC(12;21;28) 

12 = 2².3 ; 21 = 3.7; 28 = 2².7 => BCNN (12;21;28) = 2².3,7 = 84

=> x ∈ {0;84; 168; 252; 336;...} 

Vì 150 < x < 300 nên x = 168 hoặc x = 252

ta có : 144=2⁴.3²

Bài 1 : ta có : 192=2⁶.3 và 144=2⁴.3²

Vậy ƯCLN_(144;192)=2⁴.3=48

Vậy ƯC_(144;192)={1;2;3;4;6;8;12;16;24;48}

Vậy các số cần tìm là : 24;48

\(1,\) Ta có \(144=3^2\cdot2^4;192=3\cdot2^6\)

\(\RightarrowƯCLN\left(144;192\right)=3\cdot2^4=48\)

\(\Rightarrow a\inƯ\left(48\right)=\left\{1;2;34;6;8;12;16;24;48\right\}\)

Mà \(a>20\)

\(\Rightarrow a\in\left\{24;48\right\}\)

2^x+3+2^x=144

2^x.(2³+1)=144

2^x.9=144

2^x = 144:9

2^x=2⁴

=> x=4

\(2^x.2^3+2^x.1=144\)

\(2^x.\left(2^3+1\right)=144\)

\(2^x.9=144\)

\(2^x=144:9\)

\(2^x=16\)

\(2^x=2^4\)

Vậy x=4

\(2^{x+3}+2^x=144\)

\(=>2^x\left(2^3+1\right)=144\)

\(=>2^x.9=144\)

\(=>2^x=2^4=>x=4\)

=> (x-2)x 153= 144x 255

<=> (x-2). 153= 36720

<=> x-2 = 240

<=> x= 242

\(Vi`\frac{x-2}{255}=\frac{144}{153}\)

\(\Rightarrow\left(x-2\right)153=144.255\)

\(\Rightarrow\left(x-2\right)153=36720\)

        \(\Rightarrow\left(x-2\right)=240\)

                      \(\Rightarrow x=242\)