Investment Problem?

Question

I'm trying to solve this investment problem when two accounts are equal. I get the two equations set equal to each other.
4600e^0.073t = 7500e^0.040t
I need to solve this for t but I never can get it right. How do you get t? I'm having a total brain freeze.

Answer 1

Take the log of both sides:
ln (4600e^(0.073t)) = ln (7500e^(0.040t))
ln 4600 + ln e^(0.073t) = ln 7500 + ln e^(0.040t)
ln 4600 + 0.073t = ln 7500 + 0.040t
0.033t = ln 7500 - ln 4600
33t/1000 = ln (7500/4600)
t = 1000 ln (75/46)/33
t ≈ 14.81353688

Answer 2

take log and solve