[tex]5^{x+2}+5^{x+1}+5^x\cdot x=102x+3819\\
5^x(25+5+x)=102x+3819\\
5^x(30+x)=102x+3819\\
u(5^x)= 5=\ \textgreater \ u(5^x(30+x))=0\ sau\ 5\\
1)u(5^x(30+x))=0=\ \textgreater \ u(102x)=1(imposibil)\\
2)u(5^x(30+x))=5=\ \textgreater \ u(102x)=6=\ \textgreater \ u(x)=3\ sau\ 8\\
Singurul\ numar\ natural\ care\ verifica\ ecuatia\ este\ 3.[/tex]