Solve the following problems without using a calculator. Show all your work! No work will result in no credit. log 0.001-3 log 0.016=-1.796 log 10 log 13= 1.114 log 20 = 1.301 log 100 = 2 log 50, 000= 4.699 log 1,000,000=6 a) Using the table above, calculate log 2000. b) Using the table above, calculate log 0.013. c) Solve the following equation for r: log(r+3)-log(r-3)=2. Simplify and leave your answer in fraction form. d) Use the table to rewrite the following as a single logarithm that does not include fractions 2+ log r+log 7. The half-life of caffeine in the body is about 5 hours. The average cup of coffee has 100 mg. of caffeine. While cramming for an exam. Priya drank 4 cups of coffee. a) Write a function, C(h), which calculates how much caffeine is left in Priya's body after h hours. b) Priya estimates that she will not be able to fall asleep until she has less than 30 mg. of caffeine left in her body. How many hours will it take for this to happen? c) The average cup of green tea has 40 mg. of caffeine. Rewrite the equation from part (a) as if Priya been drinking green tea instead of coffee. d) Using the equation from part (e), how many hours will it be until Priya is able to fall asleep?