Principles of Math 12: Logarithms Practice Exam 1

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1 Principles of Math 1: Logarithms Practice Eam 1

2 Principles of Math 1 - Logarithms Practice Eam Use this sheet to record your answers NR NR 7. NR 1. NR NR Copyright Barry Mabillard, Principles of Math 1: Logarithms Practice Eam

3 1. The graph of f ( ) Logarithms Practice Eam = b and the graph of reflections of each other about the line A. y = B. y = b C. = 0 D. y = 0 1 g ( ) =, where b > 0, are b Use the following information to answer the net question. Equation I log y = log 3 Equation II y = 3 Equation III y = 6 Equation IV ( 6) y = 3. A solution to the equation log3 = 6 could be approimated using technology by graphing equations A. I and III B. I and IV C. II and III D. II and IV 1 3. The epression log A. log5 B. log 1 5 C. log ( 5 ) D. log5 is equivalent to Principles of Math 1: Logarithms Practice Eam 3

4 Use the following information to answer the net question. The power rating of a particular dynamic electronic circuit is given by the equation P= t w where P is the power rating, t is amount of time since the circuit is switched on, and w is a constant. 4. After the circuit has been operational for 43 seconds, the power rating is The value of w, to the nearest hundredth, is A B. 0.5 C D The epression log ( 3 ) ( y z log y ) A. log ( 3 yz) y B. log z C. 3log y + log z log y+ log z D. 1 z is equivalent to 4 6. The value of b in the equation 7= 3 +b) is equivalent to A. log B. log4 7 log C. 7 3 D ( Numerical Response 1. If y = 8, then to the nearest tenth, the value of 5log + 5log y is. Principles of Math 1: Logarithms Practice Eam 4

5 3 7. The solution to the equation = 5 1, correct to the nearest hundredth, is A B C D Use the following information to answer the net question. The mass of a radioactive sample is represented in the graph below. The initial mass of 3 mg decays to 8 mg after 1 hours. 8. The half-life of the radioactive sample, in minutes, is A. 60 B. 40 C. 630 D. 160 Numerical Response. 5 a Given ( log ) a = c, the value of, to the nearest hundredth is. c Principles of Math 1: Logarithms Practice Eam 5

6 Use the following information to answer the net question. The graph of a function g() is shown below 9. If the graph of g() is transformed to a new graph h(), and the point (0, a) becomes (a, 0), then a possible transformation is 1 A. h ( ) = g ( ) B. h ( ) = ag ( ) C. h ( ) = g ( ) + a D. 1 h ( ) = g ( ) + a 10. A skilled player at the video game Dot Gobbler has an average high score of points. For every day the player is on vacation, she can epect to lose.7% of her gaming ability. An equation that may be used to predict the average score S of the player after d days is A. S = 50000(.7) 1 d B. S = 50000( 0.07) d C. S = 50000( 0.973) 1 d D. S = 50000( 0.973) d Principles of Math 1: Logarithms Practice Eam 6

7 Use the following information to answer the net two questions. The decibel level of a sound may be calculated using the formula 1 ( I) L= 10log 10 where L is the loudness of the sound (db) and I is the intensity of the sound. 11. An equation that can be used to solve for the value of I is A. B. C. L I = 10 log10 L I = log I = 10 L I = 10 D. 13 L The loudness of a jet engine is 150 db. The magnitude of the sound intensity is A B C D Numerical Response 3. 1 The epression log b 100 b is equivalent to a numerical value of. Principles of Math 1: Logarithms Practice Eam 7

8 13. The inverse of f ( ) = 3 +4 is A. 1 f ( ) = B. 1 f ( ) = log3 ( 4) C. 1 f ( ) = 4 3 D. 1 f ( ) = log ( 3) The graph of ( ) y =, where b < 0, is the same as the graph of b A. y = log b reflected in the line y = B. y = log b reflected in the line y = C. y = log b reflected in the line y = 0 D. y = b Use the following information to answer the net question. Newton s Law of cooling can be represented by the equation Tt () = Te kt 0 where T(t) is the final temperature in degrees Celsius, T 0 is the initial temperature in degrees Celsius, t is the elapsed time in minutes, and both e & k are constants. e =.718 k = Numerical Response 4. The length of time, in minutes, required for a cup of coffee to cool from 8 C to 65 C is. Principles of Math 1: Logarithms Practice Eam 8

9 Use the following information to answer the net four questions. The graph of f( ) = 4 is shown below 15. The graph of f( ) = 4 and the graph of g ( ) = log4 are symmetrical with respect to the line A. = 0 B. y = 0 C. y = D. y = If the graph of g ( ) log 4 undergoes the transformation y = g 3 1 +, the new domain of the graph is A. > B. > 3 C. > 4 D. > 1 = ( ) 17. A student wishes to solve the equation 4 = 8. An incorrect procedure to determine the solution is A. Take the logarithm of both sides, use the power rule of logarithms, then isolate the variable by dividing both sides of the equation by log 4. B. Graph y 1 = 4 and y = 8 in a graphing calculator, find the point of intersection, then state the y-value of this point as the solution. C. Draw y 1 = 4 and y = 8 carefully on graph paper, then approimate the coordinates of the point of intersection. D. Find a common base for each side of the equation, then simplify and solve. Principles of Math 1: Logarithms Practice Eam 9

10 18. The equation 4 y = is represented by graph A. B. C. D. 19. The equation f ( ) 7a + = b, has an intercept equivalent to log b log 7 A. = log a = 7a b B. y+ b C. = 7a D. = 0 Principles of Math 1: Logarithms Practice Eam 10

11 0. A student solves for a in the equation log7 ( 81a) = b. The student determines a is equivalent to the epression A. log81 a = blog 7 B. 3 4 a 3 b = C. b a = 7 81 D. a = 3 1. Given the equation a 5 4 = b, an epression for a is A. 4 5 b B. ( b ) 4 5 C. D. 4 b 5 1 ( b) 4 5 Use the following information to answer the net question. A student analyzes the following graph: ( ) = log ( 6 ) f. The domain of this graph is A. < 0 B. < 6 C. 0< < 6, 1 D. 1< < 6 3. The -intercept of the graph y = blog c a is A. a 1 B. a C. = 0 D. b Principles of Math 1: Logarithms Practice Eam 11

12 Numerical Response 5. Given the equation log + 3log = 8, a student determines the value of to be. 4. One third of 3 34 is A B C D Given the equation log + y = log z, an epression for y is A. y = log a z B. z y = log a y = log a z D. y = z C. ( ) a a 6. The price of a vintage video game with the bo and instructions doubles every 0 years. If the video game initially cost $60.00, the value of the game in 33 years will be A B C D Principles of Math 1: Logarithms Practice Eam 1

13 7. The population of a city can be determined using the equation P = (1.03) t where P is the future population, and t is the time in years. An equation representing t as a function of P is A. P t = B. t = log P 5 log1.03 C. log P t = 5log1.03 D. log P 5 t = log The value of in the equation ( ) ( ) A. = -1 B. = 1 C. =± 1 D. No Solution log + log + = log 3 is 1 9. If log6 = 10, then log6 36 is A. 0.5 B C. 84 D. 118 a a is logbc logbc 30. An epression equivalent to ( )( ) A. a + a logb c B. ( ) log b c a C. D. logb a c b logc a Principles of Math 1: Logarithms Practice Eam 13

14 31. The graph of y = b, where b < 1, undergoes the transformation y+ 3 = f( ). The range of the transformed graph is A. y < 3 B. y > 3 C. y 3 D. y 3 3. The solution of ( ) ( ) A. -4 B. 3 C. -4, 3 D. No Solution log + + log 1 = 1 is Principles of Math 1: Logarithms Practice Eam 14

15 Written Response 10% 1. Draw the graph of f ( ) log( ) = + in the space provided below Complete the following chart to describe the graph above Domain Range Equation of Asymptote -intercept y-intercept y-value when = Describe the transformations applied to the graph of y = log in order to obtain the graph of f ( ) = log( + ) The domain of the general epression f ( ) = alog( b+ c) + d is Principles of Math 1: Logarithms Practice Eam 15

16 Use the following information to answer the net question. A student is asked to solve the equation 7 81 = 43 using different techniques learned in Principles of Math 1. Written Response 10%. Eplain how to solve the equation graphically. Indicate appropriate window settings and state the solution. Algebraically show how to solve this equation using a common base. Algebraically show how to solve this equation by taking the logarithm of both sides and solving for. The student is now asked to solve the equation log 3 = 4. Eplain how this can be done with a graphing calculator. Principles of Math 1: Logarithms Practice Eam 16

17 Use the following information to answer the net question. A useful equation for solving application questions is 0 ( ) A= A b where A is the future amount, A 0 is the initial amount, b is the rate of growth or decay, P is the period, and t is the elapsed time. t P Written Response 10% 3. Algebraically solve for P A particular bacteria doubles every P hours. If a bacterial culture starts with bacteria and has bacteria after 3 hours, determine the doubling period. The population of a town triples every 8 years. Determine the number of years it will take for the population to double. Principles of Math 1: Logarithms Practice Eam 17

18 Light passing through dirty water retains only ¾ of its intensity for every metre of water. Determine the depth at which the light will have 64% of its surface intensity. A particular painting goes down in value by 4.3% each year due to improper storage. Determine the number of years it will take for the value of the painting be half the initial worth. You have now completed the eamination. Please check over your answers carefully before self-marking. Good luck on your real eam! Principles of Math 1: Logarithms Practice Eam 18