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

         2^2x.3^y=144

        2^2x.3^y=16.9(có thể là bằng 3.48 nhưng nó không hợp lệ) 

nếu : 2^2x.3^y=16.9

         2^2x=16 thì x=2     ;3^y=9 thì y=2

 (2^2x không thể bằng 9 đk vì không có số nào 2^2x=9 đk cả)

\(a,2^x+2^{x+3}=144\\ 2^x.\left(1+2^3\right)=144\\ 2^x.9=144\\ 2^x=144:9\\ 2^x=16=2^4\\ vậy:x=4\)

\(b,\left(x-5\right)^{2022}=\left(x-5\right)^{2021}\\ Vì:\left[{}\begin{matrix}0^{2022}=0^{2021}\\1^{2022}=1^{2021}\end{matrix}\right.\\ Vậy:\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

\(c,\\ \left(2x+1\right)^3=9.81\\ \left(2x+1\right)^3=3^2.3^4\\ \left(2x+1\right)^3=3^6\\ \left(2x+1\right)^3=\left(3^2\right)^3=9^3\\ Vậy:2x+1=9\\ 2x=9-1\\ 2x=8\\ x=\dfrac{8}{2}\\ x=4\)

2^x+2^x+3=144

2^x+2^x.2³=144

2^x.(1+2³)=144

2^x.9=144

2^x=144:9

2^x=16

2^x=2⁴

=> x=4

Vậy x=4

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

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

\(2^x.9=144\)

\(2^x=16\)

\(2^x=2^4\)

\(\Rightarrow x=4\)

2^x+2^x+3=144

\(\Rightarrow2^x+2^x.2^3=144\)

\(\Rightarrow2^x.\left(1+2^3\right)=144\)

\(\Rightarrow2^x.9=144\)

\(\Rightarrow2^x=144:9\)

\(\Rightarrow2^x=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

Vậy x=4

Chúc bn học tốt

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 \(x\in\left\{12;16;24;48\right\}\)

(2x + 1) . (2x + 2) . (2x + 3) . (2x + 4) - 5y = 11879

[(2x + 1). (2x + 4)].[(2x + 2) . (2x + 3)] -5y = 11879

(4x²+10x+4).(4x²+10x+6) -5y = 11879

Đặt t= 4x²+10x+4

t(t+2) -5y = 11879

t²+2t-5y = 11879

(t+1)² = 11880+5y

(4x²+10x+5)² = 5(2376+y)

=> x = 0; y=-2371

thanks

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