Question

Tìm các số nguyên tố x và y biết:

a) \(5.2^{x+1}.2^{-2}-2^x=384\)

b) \(3^{x+2}.5^y=45^x\)

c) \(\left(x+1\right)^{x+1}=\left(x+1\right)^{x+1}\)

d) \(27< 3^x< 243\)

Answer 1

a) \(5.2^{x+1}.2^{-2}-2^x=384\Leftrightarrow2^x\left(5.2^{-2}.2-1\right)=384\)\(\Leftrightarrow2^x.1,5=384\Leftrightarrow2^x=384:1,5=256=2^8\)

\(\Rightarrow x=8\)

b) \(3^{x+2}.5^y=45^x\Leftrightarrow3^{x+2}.5^y=3^{2x}.5^x\Leftrightarrow\frac{3^{2x}}{3^{x+2}}=\frac{5^y}{5^x}\)\(\Leftrightarrow3^{2x-x+2}=5^{y-x}\Leftrightarrow3^{x+2}=5^{y-x}\)

\(\Rightarrow x+2=y-x=0\Rightarrow x=y=-2\)