Question

tìm số nguyên x, nếu biết:

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

Answer 1

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(\Rightarrow4^{x+1}.\left(4^2-3\right)=13.4^{11}\)

\(\Rightarrow4^{x+1}.\left(16-3\right)=13.4^{11}\)

\(\Rightarrow4^{x+1}.13=13.4^{11}\)

\(\Rightarrow x+1=11\)

\(\Rightarrow x=11-1\)

\(\Rightarrow x=10\)

Answer 2

\(\Rightarrow4^x\left(4^3-3.4\right)=13.4^{11}\)

\(\Rightarrow4^x.52=13.4^{11}\)

\(\Rightarrow4^x=4^{\left(-1\right)}.4^{11}\)

\(\Rightarrow4^x=4^{10}\)

=> x=10

Answer 3

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(\Leftrightarrow4^{x+1}.4^2-3.4^{x+1}=13.4^{11}\)

\(\Leftrightarrow4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(\Leftrightarrow4^{x+1}.13=13.4^{11}\)

\(\Leftrightarrow4^{x+1}=4^{11}\)

\(\Leftrightarrow x+1=11\)

\(\Leftrightarrow x=10\)

Answer 4

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(\Leftrightarrow4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(\Leftrightarrow13.4^{x+1}=13.4^{11}\)

\(\Leftrightarrow4^{x+1}=4^{11}\)

\(\Leftrightarrow x+1=11\)

\(\Leftrightarrow x=10\)

Answer 5

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(\Rightarrow4^{x+1}.4^2-3.4^{x+1}=13.4^{11}\)

\(\Rightarrow4^{x+1}.\left(4^2-3\right)=13.4^{11}\)

\(\Rightarrow4^x.13=13.4^{11}\)

\(\Rightarrow4^x=4^{11}\) ( chia cả 2 vế cho 13 )

\(\Rightarrow x=11\)

Vậy x = 11