4000=500e^1.5r what is the answer?
Take logs of both sides (Natural logs)
ln(4000) = ln(500) + ln(e^1.5r)
ln(4000) = ln(500) + (1.5r)*ln(e)
ln(4000) = ln(500) + 1.5r
ln(4000) - ln(500) = 1.5r
r = {ln(4000) - ln(500)} /1.5
evalusting this,
r = {8.29405 - 6.21461} /1.5
r ={2.07944} / 1.5
r = 1.38629
N.B. you can also divide 4000 by 500 first of all to give 8 = e^(1.5r), then take logs of both sides.
If you have an expression that you have to solve and it's got powers in it, then it's sometimes a good idea to take logs of both sides.