Solve for ttt: 1000=500(1.02)t1000 = 500(1.02)^t1000=500(1.02)t.
t=ln2ln1.02t = \frac{\ln 2}{\ln 1.02}t=ln1.02ln2
t=ln1.02ln2t = \frac{\ln 1.02}{\ln 2}t=ln2ln1.02
t=2ln(1.02)t = 2 \ln(1.02)t=2ln(1.02)
t=ln(2)+ln(1.02)t = \ln(2) + \ln(1.02)t=ln(2)+ln(1.02)