Question

Tìm x thuộc số tự nhiên biết:

4^x+2+2^2x+1=1152

Answer 1

\(4^{x+2}2^{2x+1}=1152\)

\(\Rightarrow4^x.4^2+2^{2x}.2^1=1152\)

\(\Rightarrow4^x.4^2+4^x.2=1152\)

\(\Rightarrow4^x\left(4^2+2\right)=1152\)

\(\Rightarrow4^x=1152:\left(4^2+2\right)\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^3\)

\(\Rightarrow x=3\)

Answer 2

\(4^{x+2}+2^{2x+1}=1152\)

\(\Rightarrow2^{2x+4}+2^{2x+1}=1152\)

\(\Rightarrow2^{2x+1}.\left(2^3+1\right)=1152\)

\(\Rightarrow2^{2x+1}.9=1152\)

\(\Rightarrow2^{2x+1}=128\)

\(\Rightarrow2^{2x+1}=2^7\)

\(\Rightarrow2x+1=7\)

\(\Rightarrow x=3\)

Vậu x = 3

Answer 3

\(4^{x+2}+2^{2x+1}=1152\)

\(\Rightarrow4^x.4^2+2^{2x}.2=1152\)

\(\Rightarrow4^x.4^2+\left(2^2\right)^x.2=1152\)

\(\Rightarrow4^x.4^2+4^x.2=1152\)

\(\Rightarrow4^x.\left(4^2+2\right)=1152\)

\(\Rightarrow4^x.\left(16+2\right)=1152\)

\(\Rightarrow4^x.18=1152\)

\(\Rightarrow4^x=64\)

\(\Rightarrow4^x=4^3\)

\(\Rightarrow x=3\)

Vậy \(x=3\)