Question

2^x+2^x+1+2^x+2+2^x+3=480

Answer 1

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)

\(\Leftrightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=480\)

\(\Leftrightarrow2^x\left(1+2+2^2+2^3\right)=480\)

\(\Leftrightarrow2^x.15=480\)

\(\Leftrightarrow2^x=32=2^5\)

\(\Leftrightarrow x=5\)

Answer 2

2^x + 2^{x + 1} + 2^{x + 2} + 2^{x + 3} = 480

15 . 2^x = 480

2^x = 480 : 15

2^x = 32

2^x = 2⁵

=> x = 5