Question

For questios #230.6.c. solve fort and leave answer in exact form (no calculator allowed...no need for decimal answers). Only an algebraic solution will be accepted. a. 5(1.15)' = 8(1.07) b. 3in(2t) = 12 (leave answer in terms of e) c.log(t-15) + log t = 2

Answer 1

(a) s(115)- 8 (104)+. apply log on both sides ( dog (s. (115)). log (8 (107)t) t log (9), . this is in the form log (96) = logla) + log lb) = log (5) + log (115) t- log(s) + log (103)+ we know log at = log (5) + t log (11s) - log (3) + t log (107) - log(s) - log/s) = t log (115) t log11:07) Teogle). log(o) = logl/b] >> loy (s/s) - t log (115/104) ode PA 10 ta log 18/s) lud PET doy (15) 1-07) (6) 3 ln (at) - 121 I natah Loft a bit et apply exponention on both sides ln 12t) = 12 13

ln (2 t) - 4 & lift (at) - e4 at=e4 t=e4 2

(c) log (1-15) + log It) a log (4) + log (6) = loglan] Joyllt-is) (t) = 2 lag (12-15L) = 3 apply 10 power on both sides. to log (t²-1st) = 102 2-150=100 1²-15t - 100 =0 12- 204 +5-100 -0. 1 t12-20) +5 11-20)=0 (E+)14-20) - ale t=-5 t=20