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

\(\Leftrightarrow2^x+2^x.2^3=144\)

\(\Leftrightarrow2^x+2^x.8=144\)

\(\Leftrightarrow2^x.\left(1+8\right)=144\)

\(\Leftrightarrow2^x.9=144\)

\(\Leftrightarrow2^x=16\)\(\Leftrightarrow2^x=2^4\)

\(\Leftrightarrow x=4\)

Vậy \(x=4\)

       2ⁿ⁺³.2ⁿ =144

\(\Leftrightarrow\)2ⁿ.2³.2ⁿ=144

\(\Leftrightarrow\)2²ⁿ.8=144

\(\Leftrightarrow\)2²ⁿ=18=2.9 (vô lý)

Vậy n\(\in\varnothing\)

2^x+2^x+3=144

2^x.1+2^x.2³=144

2^x(1+8)=144

2^x.9=144

2^x=144:9

2^x=16

2^x=2⁴

==> x=4

2^x + 2^x+3 = 144

2^x + 2^x.2³ = 144

2^x . (1 + 2³) =  144

2^x                = 144 : 9

2^x                = 16 

2^x                = 2⁴

x                 = 4

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

\(\Rightarrow2x+1+2^x.2^3=144\)

\(\Rightarrow2x.\left(1+2^3\right)=144\)

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

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

\(\Rightarrow2^x=16\)

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

\(\Rightarrow x=4\)

2ⁿ+2ⁿ⁺³=144

=>2ⁿ+2ⁿ⁺³=2⁴+2⁷

=>n+n+3=4+7

=>2n+3=11

2n=8

n=4

2ⁿ+2ⁿ⁺³=2ⁿ+2ⁿ.2³=2ⁿ(1+8)=2ⁿ.9=144

=>2ⁿ=144:9=16

=>2ⁿ=2⁴

=>n=4

vậy...

\(2^n+2^{n+3}=144.\)

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

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

\(2^n\left(1+8\right)=144.\)

\(2^n.9=144.\)

\(2^n=144:9.\)

\(2^n=16.\)

\(2^n=2^4\Rightarrow n=4\in N.\)

Vậy \(n=4.\)

CÓ THỂ LÀ RẤT KHÓ

ko phải khó mà rất khó

\(\frac{1\cdot3\cdot5\cdot\cdot\cdot\cdot\left(2n-1\right)}{\left(n+1\right)\left(n+2\right)\cdot\cdot\cdot2n}=\frac{\left[\left(1\cdot3\cdot5\cdot\cdot\cdot\cdot\left(2n-1\right)\right)\right]\left(2\cdot4\cdot6\cdot\cdot\cdot\cdot2n\right)}{\left(n+1\right)\left(n+2\right)\cdot\cdot\cdot2n\left(2\cdot4\cdot6\cdot\cdot\cdot2n\right)}\)

\(=\frac{1\cdot2\cdot3\cdot4\cdot5\cdot\cdot\cdot\cdot\left(2n-1\right)\cdot2n}{2^n\left(1\cdot2\cdot3\cdot4\cdot\cdot\cdot\cdot n\right)\left(n+1\right)\left(n+2\right)\cdot\cdot\cdot2n}\)

\(=\frac{1}{2^n}\)