Math 12 Practice Test (1) Logarithms & Exponents



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College Algebra and Trigonometry

Logarithmic and Exponential Functions Review for Test – Chp5

1) Evaluate [pic].

2) Express 3loga+logb-logc as a single logarithm.

3) Which of the following is equivalent to [pic]?

a) 2logm+logn b) [pic]

c) logm+2logn d) 2logm+2logn

4) Solve for y: [pic].

5) Write each equation in logarithmic form.

a. 4x =36 b. 2 -3 = [pic] c. e2 = x

Write each equation in exponential form.

d. log634 = 1.968 e. log232 = 5 f. ln5 =1.609

6) Solve [pic].

7) Solve [pic].

8) Solve [pic].

9) Solve for x. Show the equations you use to solve for x.

a. 5x =28 b. 8x -10 =59 c. 7 (x+3) =210

d. ex =25 e. 2ex +4 =200 f. log5x=4

g. 3 + log4 X =2 h. ln x = 3.2 i 5(x+3) -4 =75

10) On the day her niece, Hope, is born, how much should Mrs. Grace deposit in an account that earns 3.255% interest compounded continuously so that her niece , Hope, will have $40,000 in her college fund on her 18th birthday?

11) Which of the following is equivalent to [pic]?

a) [pic] b) [pic]

c) [pic] d) [pic]

12) Condense the expression.

log2(x – 4) + 5 log2(x + 1) – 3log2(x – 1)

13) Determine an expression for “x” if [pic] .

a) [pic] b) [pic] c) [pic] d) [pic]

14) Solve the logarithmic equation. Round the result to three decimal places if necessary.

a) ln(x + 3) = 10

b) log2 x + log2(x + 1) = 1

c) log2(x + 1) – log2 x = 3

15) Solve the exponential equation. Round the result to three decimal places if necessary.

a) [pic]

b) [pic]

16) The population of a bacterial culture increases as a rate of 12.5%. If the present population is 4000 bacteria, how long will it take for the population to reach

75 000? (Answer in hours accurate to nearest hundredth).

17) Solve algebraically for “x”: log(3x-5) + log(2x-1) = 1.

18) What per cent annual increase will allow a population of 2 million fish to increase to a population of 3 million over 10 years? (nearest hundredth)

19) Find the value of a signed football that was bought for $35 and its value has appreciated 8% each year after 20 years later.

20) The city planners of Boom-town electro-valley are excited, they have a population of 7,800 and it is growing at a rate of 35% every year. Find the size of their city in 10 years.

21) A tropical fish colony of 200,000 is having pollution challenges and is decreasing in size by 3.5% annually.

a) Find the population of this fish in 30 years.

b) In how many years will the colony be extinct?

22) The depreciation of the value for a motorcycle is modeled by y = 10,000(.85)x for x years since 2000. In what year was the value of the car was $6,141.25?

23) A new automobile is purchased for $20,000. If V = 2,000(0.8)x, gives the car’s value after x years, about how long will it take for the car to be worth $820?

24) A student wishes to save some money for college. How long will it take $5,000 to double in value if it is invested at a rate of 6.7% compounded continuously?

25) The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26%. Write a function to model world population growth since 2000. Predict the population in the year 2040.

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