Question

[TVVV]

\(2^{x+22}-4^{x+11}=0\) 

Answer 1

[HT.Phong (9A5)]

\(2^{x+22}-4^{x+11}=0\)

\(\Rightarrow2^{x+22}-2^{2x+22}=0\)

\(\Rightarrow2^x\cdot\left(2^{22}-2^{x+22}\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}2^x=0\left(L\right)\\2^{22}-2^{x+22}=0\end{matrix}\right.\)

\(\Rightarrow2^{x+22}=2^{22}\)

\(\Rightarrow x+22=22\)

\(\Rightarrow x=22-22\)

\(\Rightarrow x=0\)

Vậy x=0

Answer 2

[Nguyễn thành Đạt]

\(2^{x+22}-4^{x+11}\text{=}0\)

\(2^{x+22}\text{=}4^{x+11}\)

\(2^x.2^{22}\text{=}4^x.4^{11}\)

\(2^x.2^{22}\text{=}4^x.\left(2^2\right)^{11}\)

\(2^x.2^{22}\text{=}4^x.2^{22}\)

\(2^x\text{=}4^x\)

\(x\text{=}0\)