3^x *2^y = 144
log√2(y-x)=2

[tex] \left \{ {{3^x*2^y=144} \atop {log_{ \sqrt{2}}(y-x)=2 }} \right.\; \; \; y-x\ \textgreater \ 0\; \; \; y\ \textgreater \ x\\\\ \left \{ {{3^x*2^y=144} \atop {y-x=( \sqrt{2})^2 }} \right.\\\\\left \{ {{3^x*2^y=144} \atop {y-x=2 }} \right. \\\\\left \{ {{3^x*2^y=144} \atop {y=2+x }} \right.\\\\3^x*2^{2+x}=144\\3^x*2^2*2^x=144\\(3^x*2^x)*4=144\\3^x*2^x=36\\6^x=6^2\\x=2\\y=2+2=4\; \; \; (4\ \textgreater \ 2) [/tex]
Ответ: х=2; у=4