Question

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

Answer 1

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

\(\Rightarrow2^x+2^x\cdot2+2^x\cdot4+2^x\cdot8=120\)

\(\Rightarrow\left(1+2+4+8\right)\cdot2^x=120\)

\(\Rightarrow15\cdot2^x=120\)

\(\Rightarrow2^x=\dfrac{120}{15}=8=2^3\)

\(\Rightarrow x=3\)

Vậy............

Answer 2

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

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

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

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

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

\(2^x=120:15=8\)

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