Question

2^x+2^x+1+2^x+2+2^x+3=120 . Tìm x

Answer 1

2^x+2^x+1+2^x+2+2^x+3=120

2^x+2^x.2+2^x.4+2^x.8=120

2^x.(1+2+4+8)=120

2^x.15=120

2^x=120:15

2^x=8

2^x=2³

x=3

Vậy x=3

Answer 2

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)

\(\Rightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=120\)

\(\Rightarrow2^x\left(1+2+2^2+2^3\right)=120\)

\(\Rightarrow2^x.15=120\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)

Vậy x = 3

Answer 3

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)

\(\Leftrightarrow2^x\cdot1+2^x\cdot2^1+2^x\cdot2^2+2^x\cdot2^3=120\)

\(\Leftrightarrow2^x\left(1+2^1+2^2+2^3\right)=120\)

\(\Leftrightarrow2^x\left(1+2+4+8\right)=120\)

\(\Leftrightarrow2^x\cdot15=120\)\(\Leftrightarrow2^x=8\)

\(\Leftrightarrow2^x=2^3\Leftrightarrow x=3\)

Answer 4

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