.... _. m ,,_. 1 / 3 Spring 2022 Instructor: Dr. Leszczynski m Instructions: A I KEEP . is c- ' ' CALM alnd SHOW YOUR WORK This quiz focuses on logarithms and exponential and logarithmic equations. For more content related to these topics, please watch class videos and see Sections Q, Q, and 6_7 in our text. Problem 1. [1 point each] Match each expression on the le side with the equivalent expression on the right side. Write the letter of the match on the line. a) __ loyal A. 7 b) _ lne B. ilogu) C) _ 105112\" c. o d) _ 22\"\" D. 3 e) _ lne": E. 2 t) _ 5'095" F, x g) 7 log100 +log10 G. 1 h) 7 [1197 H. E i) _ ln(x+ 1)Z I. 22: j) _ logw/i J. log(3) k) _ longlog K. x2 1) _ logg9 L. 21n(x+ 1) m) loam M. 4 87% + It E] OD Problem 2. [2 points each] Find x, if it exists. If not possible, briey explain why. a. hut = 4 0.1051336 = 9 b. 5"= d.7"=7 Problem 3. [3 points each] Solve the exponential equation algebraically. Do not round your answer. No decimals, please. a, 83" = 20 h. 2e"4=10 c. 492'\" = 20 Problem 4. [3 points each] Solve the logarithmic equation algebraically. Do not round your answer. No decimals, please. a. log6(x 3) = 2 b. 3 + Zln(4x) = 13 0. [033(5): 1) 210330: + 7) Problem 5. [3 points] Use the property lagM + lagN = lagMN to nd x. log(x) + logo: + 3) = 1 /3 107% + E] Leszczynski Problem 6. Solve each problem below. a) The population of bacteria grows according to the mction P(t) = 200e'2', where t is measured in minutes. i. How many bacteria are present in the population aer 5 hours (300 minutes)? (3 pts) ii. When does the population reach 100,000 bacteria? (3 pts) The magnitude M of an earthquake is represented by the equation: M = glog (5), 0 where E is the amount of energy released by the earthquake in joules and E0 = 10"\"4 is the assigned minimal measure released by an earthquake. To the nearest hundredth, What would the magnitude be of an earthquake releasing 1.4 x 1013 joules of energy? (2 PtS)