7 Chapter Test

Do you know HOW?

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept.

1. y = 3 ( 0.25 ) x y equals 3 . open , 0.25 , close to the x
2. y = 2 ( 6 ) − x y equals . 2 open 6 close super negative x end super
3. y = 0.1 ( 10 ) x y equals 0.1 . open 10 close to the x
4. y = y equals   3 e x 3 e to the x

Describe how the graph of each function is related to the graph of its parent function. Then find the domain, range, and asymptotes.

5. y = 3 x + 2 y equals , 3 to the x , plus 2
6. y = ( 1 2 ) x + 1 y equals . open , 1 half , close super x plus 1 end super
7. y = − ( 2 ) x + 2 y equals . negative open 2 close super x plus 2 end super

Write each equation in logarithmic form.

8. 5 4 = 625 5 to the fourth , equals 625
9. e 0 = 1 e to the , equals 1

Evaluate each logarithm.

10. log 2 8 log base 2 , 8
11. log 7 7 log base 7 , 7
12. log 5 1 125 log base 5 . 1 over 125
13. log 11 1 log base 11 , 1

Graph each logarithmic function. Compare each graph to the graph of its parent function. List each function's domain, range, y-intercept, and asymptotes.

14. y = log 3 ( x − 1 ) y equals , log base 3 , open x minus 1 close
15. y = 1 2 log 3 ( x + 2 ) y equals , 1 half . log base 3 , open x plus 2 close
16. y = 1 − log 2 x y equals 1 minus , log base 2 , x

Write each logarithmic expression as a single logarithm.

17. log 2 4 + 3 log base 2 , 4 plus 3   log 2 9 log base 2 , 9
18. 3 log a − 2 log b 3 log eh minus 2 log b

Expand each logarithm.

19. log 7 a b log base 7 . eh over b
20. log 3 x 3 y 2 log . 3 x cubed . y squared

Use the properties of logarithms to evaluate each expression.

21. log 9 27 − log 9 9 log base 9 , 27 minus , log base 9 , 9
22. 2 log 5 + log 40

Solve each equation.

23. ( 27 ) 3 x = 81 open 27 close super 3 x end super . equals 81
24. 3 x − 1 = 24 3 super x minus 1 end super . equals 24
25. 4 e 2 x = 16 4 , e super 2 x end super . equals 16
26. 2 log x = − 4 2 log x equals negative 4

Use the Change of Base Formula to rewrite each expression using common logarithms.

27. log 3 16 log base 3 , 16
28. log 2 10 log base 2 , 10
29. log 7 8 log base 7 , 8
30. log 4 9 log base 4 , 9

Use the properties of logarithms to simplify and solve each equation. Round to the nearest thousandth.

31. l n 2 + ln x = 1 l n 2 plus ln x equals 1
32. l n ( x + 1 ) + ln ( x − 1 ) = 4 l n open x plus 1 close plus ln open x minus 1 close equals 4
33. l n ( 2 x − 1 ) 2 = 7 l n . open 2 x minus 1 close squared . equals 7
34. 3 ln x − ln 2 = 4 3 ln x minus ln 2 equals 4

Do you UNDERSTAND?

35. Writing Show that solving the equation 3 2 x = 4 3 super 2 x end super , equals 4  by taking the common logarithm of each side is equivalent to solving it by taking the logarithm with base 3 of each side.
36. Open-Ended Give an example of an exponential function that models exponential growth and an example of an exponential function that models exponential decay.
37. Investment You put $1500 into an account that pays 7% annual interest compounded continuously. How long will it be before you have $2000 in your account?

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