The answer to this should be 201.7, but I keep getting off track.

Question

300=70+(375-70) e^ -k*10
230=305 e^-10*k
ln 230=ln 305 e^-10*k
ln 230= ln 305 -10*k

Answer 1

yes, you do get off track.
Line 3 should be
(because ln ab = ln a + ln b)

ln 230=ln 305 + ln( e^-10*k)
ln 230 - ln 305 = -10k

because ln(e^x) = x
now go from there.

In fact, I'd have divided first:

230=305 e^-10*k
230/305 = e^-10k

Answer 2

201.7? I get nothing like that

.75 = e^-10k
-10k = -.287
k = .0287

There must be something wrong with the way you wrote the problem.

I mean e^(-10*201.7) = a very very very tiny number. Some missing parentheses?