I. Solve for x. 42-3 . 8 - 13 2. Evaluate the following logarithm (a) log . 98 - los ; 7 (b) log 200 - log 2 (c) log1050 - log 105(d) logo 25 - logo75 (e) 251085 + Blogs V5 Of log Vio (g) log 25 + log 4 (1) 2 549 () 1000 loss\f5. Solve for x and check for any extraneous roots (a) logxx +logs(x + 2) - 1 (b) log (x+3) - log(2x-1) - -16. A sum of $20,000 is invested in an account at a nominal rate of 6% annually. How much is in the account after 5 years if the interest is compounded a) annually (b) quarterly (c) monthly (d) continuously A = PelAn amount of $10,000 is deposited into an account that earns 4 % interest compounded quarterly. Let A(t) represent the balance (in thousands of dollars) in the account after t years or any fraction thereof. (a) Find a formula for A(t) (b) Find the balance after 10 years. (c) What is the doubling-time? (a) A(!) = 10000 1 0.04 (b) (c) 10000 1 - 0.04 4 - 20000 (1.01)" -2 log (1.01)" = log 2A particle decays at a rate of 0.45% annually. Assume and initial amount of 300 (a) How much of the particle remains after 60 years? (b) What is the half-life of the particle? (a) 4=300e-0.0045 A = 300e-0.064360) A = 300 e-0 0045 60) A=300e-0.27 1 = 229 mg 300 2 0045 = 150 = 0.5 In e-0.0045 = In 0.5A colony of bacteria grows according to the law N = Noe". At the start of a certain experiment there was 144 bacteria present. Eight hours later it was observed that the colony has grown to 720. What was the size of the population 6 hours after the start of the experiment? When 1 =0 N = 144ek When t - 8 720 - 144ek(8) 720 = 14484 5 - git In5 - Ine In5 - 8k k = = = 0.2012 8 When t - 6 N - 48110. The half-life of a certain radioactive substance is 16 days. An initial amount of 30 grams is obtained for a medical treatment. What is the amount of the substance after 9 days? [Use N = Noel] N = 30ek When t = 16 30ek(16)- 15 N = 30g-0.043321 61 1. Evaluate the following logarithm without the use of a calculator. (a) log 10 (b) Inve (c) 1000 loss (d) e 2last 12. Use the properties of logarithm to express as sum or difference Ve (a) In (b) In a - In ve - Inxle" In In12. Use the properties of logarithm to express as sum or difference ( a ) in ve (b) In a 2 + 2 - In ve -Inxe2* In 2 1 2 1 - -[ In(at -x7)- In(a' + =]) ] 4-21x - 2x -In(a - x) + - In(a + x) -=In(a' +=3)13. Use the fact that In 2 = 0.6931, In 3 = 1 0986, and In 5 = 1.6094 to estimate In V7.2 In v72 - b( 7.2) -= ( 7.2) 36 = In 36 In In[ In 36 - In 5] 0.987014. If in x = t and In y = u, write the following in terms of t and u. In In re Inxe' - ly+In x -1+2 -u17. Evaluate the following logarithm without the use of a calculator (a) log v1000 (b) In east (c) 25 2 1 18. Use the change of bases formula to estimate the value of log , 17 to four decimal places log 219. If log x - a , log y = b and log = = c. write log-/10xy= in terms of a,b, and c. log ,/10xy= = log( 10m=) 4 log 10xy=20. Show that (log , 7)(log , 3)(log , 50)) - 2 +log, 2 (log s 7)(log - 3)(log , 50))_ log\\7 . log 3 log 50 log 5 log 7 log 3 log 50 log 5 - 2 + logs2