The equation to solve is
100 = 64 - 46(cos(pi*t/5)) with t in [0,10]
Then 100 - 64 = -46cos(pi*t/5)
-18/23 = cos(pi*t/5)
Then pi*t/5 = cos^-1(-18/23)
pi*t = 12.3482088
hence t = 12.3482088/pi
t = 3.93 minutes
Re-arranging what you've written,
6^.05x = (83-29)/3 = 18.
Take the logs of both sides:
.05xlog(6) = log(18)
Therefore x = [log(18)/log(6)] / .05
x = 32.26294 (5dp)