Question

1. Evaluate log5625 using the following methods.
   1. By switching from logarithmic to exponential form
   2. By cancelling the base with the log base
   3. By using the "change of base" rule
2. Simplify and evaluate each of the following expressions using the laws of logarithms.

   1. log62+log618

   2. log4256+log42−log48

   3. log2128−3log24

3. Solve each of the following equations.

   1. logx81=2

   2. log12x=3

   3. log7(2x−5)=3

Task 2: Thinking questions

5. Use systematic trial and error to evaluate log35.
6. A culture of bacteria doubles every three hours. The initial culture contains 500 bacteria.
   1. How many bacteria will there be after 27 hours?
   2. How long will it take for the culture to reach 16 000 bacteria?
7. Complete the following comparison of two functions.
   1. Create a table of values for each exponential function: y=4x and y=(14)x. Use x-values of 2, 1, 0, –1, and –2. Then, graph the equations on the same grid. Include each table of values and graph in your solution.
   2. Indicate which graph represents exponential growth and which represents exponential decay.
   3. List the similarities and differences between the graphs.

Task 3: Communication questions

8. Explain the difference between the exponential form, the radical form, and the logarithmic form of an equation, and give an example of each.
9. Define a common logarithm.
10. A fellow classmate is having difficulty solving the following expression involving logarithms. List the steps you would take to solve for "x."

    log39+log32x2=log3162

11. Explain why there is no solution for the equation log20=x. Use a graph to justify your answer.
12. Use Equation Editor to correctly type and evaluate the expression: common log of the square root of 925. Round your answer to two decimal places.

Task 4: Application questions

13. The pH of coffee is 5.2 and the pH of orange juice is 4.4. How many times more acidic is orange juice than coffee? Round your answer to one decimal place.
14. An earthquake with a magnitude of 5.4 is 39 times as intense as an aftershock that occurs five hours later. What is the magnitude of the aftershock? Round your answer to one decimal place.
15. The intensity of the sound of a jet engine is 140 dB, while the intensity of the sound of a motorcycle is 100 dB. How many times louder is a jet engine than a motorcycle?
16. A new car worth $18 000 depreciates at a rate of 8% per year. Round your answers for the following questions to the nearest whole number.
    1. What will the car be worth after four years?
    2. When will the car be worth half of its value?

Answer 1

Due to the time barrier, I tried my best to solve as many questions I can.