Question

\(8^x:2^x=16^{2011}\)

Answer 1

\(8^x:2^x=16^{2011}\)

\(\Leftrightarrow\left(2^3\right)^x:2^x=\left(2^4\right)^{2011}\)

\(\Leftrightarrow2^{3x}:2^x=2^{8044}\)

\(\Leftrightarrow2^{2x}=2^{8044}\)

\(\Rightarrow2x=8044\)

\(\Rightarrow x=4022\)

Answer 2

8^x : 2^x = 16²⁰¹¹

(2³)^x : 2^x = (2⁴)²⁰¹¹

2^3x : 2^x = 2⁸⁰⁴⁴

=> 3x-x=8044

=>    2x=8044

=>     x=8044:2

=>     x=4022