Question

Câu 3:

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

b)\(\left(\dfrac{1}{2}+\dfrac{1}{3}+.....+\dfrac{1}{2013}+\dfrac{1}{2013}\right).x=\dfrac{2012}{1}+\dfrac{2011}{2}+\dfrac{2010}{3}+.....+\dfrac{2}{2011}+\dfrac{1}{2012}\)

Answer 1

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

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

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

\(\Leftrightarrow\)\(2^x\left(1+2+4+8\right)=480\)

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

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

\(\Leftrightarrow2^x=32\)

\(\Rightarrow2^x=2^5\)

\(\Rightarrow x=5\)

Vậy x = 5.