Rich – AAT(H)
Name: _________________________________
Review Unit 2 Part D Log & Exponential Functions Test
Date: _____________________ Period: _______
NON-CALCULATOR PORTION
LT 2.D.2: convert logarithm functions to exponential functions and vice versa.
#1 – 4: Write the following exponential equations as logarithmic equations.
1

1
1. 63  216
2. 9 2 
1. _________________________
3
2. _________________________
3. 2x  16
3
4. e  20.0855...
3. _________________________
4. _________________________
#5 – 8: Write the following logarithmic equations as exponential equations.
1
1
5. log5 125  3
6. log 36  
5. _________________________
6
2
6. _________________________
7. ln x  3
8. log10000  4
7. _________________________
8. _________________________
LT 2.D.1: recognize and evaluate logarithmic and natural logarithmic functions. LT 2.D.3: use the properties of logs and natural
logs to simplify expression.
#9 – 12: Evaluate each exponential or logarithmic function.
9. log 4
1
16
10. log 9 97
9. _________________________
10. _________________________
11. lne 30
12. log 4 256
11. ________________________
12. ________________________
LT 2.D.6: use the properties of logarithms and natural logarithms to evaluate, rewrite, or simplify expressions. LT 2.D.7: use
properties of logarithms to expand and condense logarithmic expressions.
#13 – 14: Expand each logarithmic expression.
13. log2
x2y
3
z
13. _____________________________________
14. ln x 3  x  5
2
14. _____________________________________
#15 – 16: Condense to a single logarithm.
15.
1
log x  4log  x  2 
2
15. _____________________________________
16. logb 42  logb 7
16. _____________________________________
LT 2.D.6: use the properties of logarithms and natural logarithms to evaluate, rewrite, or simplify expressions. LT 2.D.7: use
properties of logarithms to expand and condense logarithmic expressions. LT 2.D.9: solve logarithmic and exponential equations.
#17 – 24: Solve each equation.
17. log4  x  1  2
18. log 36 n 
3
2
17. _______________
18. _______________
19.
1
 6 n 4
6
20. 32x  16 x2
19. _______________
20. _______________
21. log  x  4   log x  log7
1
1
22. log 4 n  log 4 81  log 4 25
4
2
21. _______________
22. _______________
23. ln 7x  2  ln 3x  2
24. log3  x  3  log3  x  2  log3 14
23. _______________
24. _______________
CALCULATOR PORTION
LT 2.D.1: recognize and evaluate logarithmic and natural logarithmic functions. LT 2.D.3: use the properties of logs and natural
logs to simplify expression. LT 2.D.5: use the change of base formula to rewrite and evaluate logarithmic expressions.
#25 – 28: Evaluate each exponential or logarithmic function. Round to the nearest thousandth, if
necessary.
25. log 5 48
26. log 5
5
3
25. ________________________
26. ________________________
27. log2 50
28. log 4 123 log12 4 3 
27. ________________________
28. ________________________
LT 2.D.6: use the properties of logarithms and natural logarithms to evaluate, rewrite, or simplify expressions. LT 2.D.7: use
properties of logarithms to expand and condense logarithmic expressions. LT 2.D.9: solve logarithmic and exponential equations.
#29 – 34: Solve each equation. Round to the nearest hundredth, if necessary.
29. log2 2x  6   log2 x  3
30. 6n2  50
29. _______________
30. _______________
31. 2y  5y2
32. 43 x1  28
31. _______________
32. _______________
33. ln x  5  3
34. e 4 x  9
33. _______________
34. _______________
LT 2.D.13: use an exponential model to solve real-life problems.
#35 – 36: Use exponential growth and decay models to compete each problem as directed.
35. After 12 hours, half of a 16-gram sample of a radio-active element remains. Find the constant k to 4
decimal places for this element for t hours, then write the equation for modeling its exponential decay.
35. ________________________
________________________
36. A savings account deposit of $150 is to earn 6.5% interest per year. After how many years will the
investment be worth $450?
36. ________________________
LT 2.D.4: graph logarithmic and natural logarithmic functions. LT 2.D.12: graph an exponential function and determine the y
intercept, domain, range, and any asymptotes.
37 – 40: Sketch the graph of each logarithmic or exponential function. Identify the x- or y-intercept,
domain, range, & asymptote of each function and describe the transformation from the parent
function.
37. f  x   e x  3
38. y  3x 1
D:__________________ R: _________________
D:__________________ R: _________________
y-int: __________ Asymptote: ______________
y-int: __________ Asymptote: ______________
Transformation: _________________________
Transformation: _________________________
39. f (x )  ln  x  3  1
40. f (x )  log1  x  2 
2
D:__________________ R: _________________
D:__________________ R: _________________
x-int: __________ Asymptote: ______________
x-int: __________ Asymptote: ______________
Transformation: _________________________
Transformation: _________________________