lg(5^x+2x-3)=x(1-lg2)
lg(5^x+2x-3)=x(lg10-lg2)
lg(5^x+2x-3)=x(lg10/2)
lg(5^x+2x-3)=xlg5
lg(5^x+2x-3)=lg5^x
5^x+2x-3=5^x
2x=3
x=3/2