1. Write in logarithmic form. Show work to support your answer

6x=30

2. Writeas an exponential equation. Show work to support your answer

x=log3log300

3. Writeas a single simplified logarithm. Show work to support your answer

log520+log510=

4. Writeas a single simplified logarithm. Show work to support your answer logn3621logn9=

5. Evaluate. Provide exact answer if possible. Otherwise, round answer to 4 decimal places, where applicable. Show work to support your answer

7log54125=

6. Solve. Provide an exact answer where possible. Otherwise, round answer to 4 decimal places where applicable. Show work to support your answer

5t=400

7. Solve. Provide an exact answer where possible. Otherwise, round answer to 4 decimal places where applicable. Show work to support your answer

logk5=31

8. Solve. Provide an exact answer where possible. Otherwise, round answer to 4 decimal places where applicable. Show work to support your answer

8log2(x+5)=32

9. Write log5(x+3)2log5(x3)+log5(x+4) as a single, simplifiedlogarithm. Show work to support your answer

10. On the grid provided on the template,graph each of the following functions. Be sue to clearly indicate the corresponding equation for each graph. For parts b) and c), be sure to describe the transformations or provide the mapping notation used to create the transformed graph. Just provide the explanations/mapping notations as answers

a)f(x)=log2x

b)u(x)=2log2(x+3)

c)n(x)=log2(2x)5

11. A particular substance is being studied. A sample of 3700 grams is being analyzed. After 15 days, the substance has decayed to 3221 grams. Assuming the substance is decaying exponentially based on its half life, determine the half life of the substance. Show work to support your answer

12. The Richter Scale, M=log(I0I)is used to represent the magnitude of an earthquake. An earthquake in Alaska measured 7.8 on the Richter Scale. This was 25 000 times more intense than a previous earthquake that occurred. What was the magnitude of the previous earthquake? Show work to support your answer

13. The function, S(d) = 93log d + 65 , relates the speed of the wind, S, in miles per hour, near the centre of the tornado to the distance that the tornado travels, d, in miles. Determine the inverse function that represents the distance the tornado travels with respect to the speed of the wind. Show work to support your answer

14. Solve. Express answers in exact form if possible. Otherwise, round answers, where applicable, to 4 decimal places. Show work to support your answer

52x34=96

15. State the restrictions on x and then solve. Express answers in exact form if possible. Otherwise, round answers, where applicable, to 4 decimal places. Show work to support your answer

log4(5x7)=log4(6)log4(x)