Question

Tìm các số tự nhiên x,y biết rằng:

a) 2^x+1.3^y=12^x

b)10^x:5^y=20^y

Answer 1

a) \(2^{x+1}\cdot3^y=12^x\)

\(\left(\frac{12}{2}\right)^x\cdot2=3^y\)

\(6^x\cdot2=3^y\)

.....chịu!

b) \(10^x:5^y=20^y\)

\(10^x=100^y\)

\(2x=y\)

Answer 2

câu a:

Ta có: 2^x+1.3^y=12^x  =>2^x+1.3^y=2^2x.3^x =>2^2x-(x+1)=3^y-x =>2^x-1=3^y-x=>y-x=0 và x-1=0 =>x=y=1

 câu b:

10^x:5^y=20^y=>10^x=(20.5)^y=>10^x=100^y=>10^x=10^2y=>x=2y

   

Answer 3

\(2^{x+1}.3^y=12^x\)

\(\Rightarrow2^{x+1}.3^y=3^x.4^x\)

\(\Rightarrow2^{x+1}.3^y=3^x.2^{2x}\)

\(\Rightarrow\orbr{\begin{cases}2^{x+1}=2^{2x}\\3^y=3^x\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x+1=2x\\y=x\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\\text{Vì y = x}\Rightarrow y=1\end{cases}}\)