Find n if t(n) is approximately 10,832 in the geometric sequence with first term 83 and a common ration 1.07

You're looking for:

83*1.07^n=10832
1.07^n=10832/83=130.506
take log and solve for n
n log(1.07)=log(130.506)
n= 71.99995 = 72 since 10832 is approximate.