Question

Tìm x biết

2^x + 2^{x + 1} + 2^{x + 2} + 2^{x + 3} - 480 = 0

Answer 1

2^x + 2^x+1 + 2^x+2 + 2^x+3 - 480 = 0

\(\Rightarrow\) 2^x + 2^x+1 + 2^x+2 + 2^x+3 = 480

\(\Rightarrow\) 2^x( 1+ 2 + 2² + 2³) = 480

\(\Rightarrow\) 2^x . 15 = 480

\(\Rightarrow\) 2^x = 32

\(\Rightarrow\) x =5

Answer 2

Có:

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}-480=0\)

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

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

\(2^x.15=480\)

\(\Rightarrow2^x=\dfrac{480}{14}=32\)

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

\(\Rightarrow x=5\)

Chúc bạn học tốt!

Answer 3

2^x + 2^x+1 + 2^x+2 + 2^x+3 - 480 = 0

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

=> 2^x(1+ 2 + 2^2 + 2^3) = 480

=>2^x(2^4-1) = 480

=>2^x . 15 = 480

=>2^x = 32 = 2^5

=>x = 5