Question

[Nguyễn Trần Linh Na]

Tìm số nguyên x, nếu biết

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

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

\(\left(\frac{1}{3}+\frac{1}{6}\right)2^{x+4}-2^x=2^{13}-2^{10}\)

\(\left(\frac{1}{2}-\frac{1}{6}\right)3^{x+4}-4.3^x=3^{16}-4.3^{13}\)

Answer 1

[Nguyễn Tấn Phát]

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}\left(5-3\right)=2.5^{11}\)

\(5^{x+3}.2=2.5^{11}\)

\(5^{x+3}=5^{11}\)

\(x+3=11\)

\(x=8\)

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

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

\(4^{x+1}.13=13.4^{11}\)

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

\(x+1=11\)

\(x=10\)