5^lgx-3^(lgx-1)=3^(lgx+1)-5^(lgx-1)
5^lgx+5^(lgx-1)=3^(lgx+1)+3^(lgx-1)
5*5^(lgx-1)+5^(lgx-1)=3²*3^(lgx-1)+3^(lgx-1)
(5+1)*5^(lgx-1)=(9+1)*3^(lgx-1)
6*5^(lgx-1)=10*3^(lgx-1)
3*5^(lgx-1)=5*3^(lgx-1)
5^(lgx-2)=3^(lgx-2)
lgx-2=0
lgx=2
x=10²=100