Question

ai giai minh bai toan tim x\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)

Answer 1

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

2^x.15=120

2^x=120:15

2^x=8

2^x=2^3

x=3

Vậy x=3

Answer 2

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

\(\left(2^x+2^{x+1}\right)+\left(2^{x+2}+2^{x+3}\right)\)

\(=\left(2^x+2^x\cdot2\right)+\left(2^x\cdot4+2^{x+3}\cdot8\right)\)

\(=2^x\cdot3+2^x\cdot12=2^x\cdot15\)

\(2^x\cdot15=120\)

\(2^x=8\)

\(x=3\)

Answer 3

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

\(\Leftrightarrow\)\(2^x.15=120\)

\(\Leftrightarrow\)\(2^x=8\)

Mà 8=2\(^3\Leftrightarrow x=2\)

Vậy x=2

Answer 4

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

\(\Rightarrow2^x.\left(1+2+4+8\right)=120\)

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

\(\Rightarrow2^x=8=2^3\)

\(\Rightarrow x=3\)