1000=500e^.05x

1000 =  500e^(.05x)

Divide both sides by 500:  2  =  e^(.05x)

Take the ln of both sides:  ln(2)  =  ln( e^(.05x) )

Since the ln( e^z )  =  z:  ln(2)  =  .05x

Divide both sides by .05:  x  =  ln(2) / .05

Use a calculator to get a decimal approximation.