Ch. 7 Review
Algebra 2
Name___________________
1. What is a logarithm?
2. Write as a logarithm:
AB  C
3. Write as an exponential equation: log M N  P
Expand each logarithm completely.
4. log3 M 4 N 2
 A2 
5. log5  3 
B 
6. log7  2 x  3
4
 7x 
7. ln  3 2 
yw 
Simplify each logarithm completely.
8. log3 7  log3 8
9. 2 log W  3log P
10. 3ln A  4ln B  4ln C
 1 
11. log5 

 125 
12. e 2 ln 7
13. log10 y1
14. log 3 1
15. ln e
Solve each equation. Use logarithms only when necessary.
If you use logarithms, write your solution in calculator ready form before using your calculator.
x
16. 42 x  32
1
17.    27 x1
9
18. 2 x  11
19. 3x2 
20. 5x  2  7 x
21. 3x 4  71 x
22. 3  5x   7
23. 3  4 x  5x
24. log4  2 x  1  3
25. log  x 2  x   log 12 
26. ln  x   ln  6  7
27. 6  e x 1
28. log  2 x   log 5  log  3
29. log3  x  5  log3  x  4   3
1
2
30. 27  10 x2
Graph each function. Include the critical point and any asymptotes.
31. y  5x
32. y  e x2
33. y  10x  3
34. y  32 x  1
35. y  log7 x
36. y  log  x  3
37. y  ln x  4
38. y  ln  x  2   3
Find the inverse function for each function given:
39.
f ( x)  2 x  8
40. g ( x )  10 x 1
41. f ( x)  ln  x  3
42. g ( x ) 
3x  2
5x  1
12 t
r 

43. Given the formula: A  P  1   , where A is the amount after t years for an initial investment of P at
 12 
an APR of r compounded monthly. How long will it take $6,000 to increase to $15,000 at an APR of 6.3%?
44. Given the formula: A  Pe rt , where A is the amount after t years for an initial investment of P at an APR
of r compounded continuously. How long will it take $6,000 to increase to $15,000 at an APR of 6.3%?
45. Given the formula: P (t )  P0e kt , where P0 is the initial population and P(t) is the population at time t and k
is the constant of growth. The population of whooping cranes was about 22 in 1940 and grew at an exponential
rate to about 194 in 2003. If the flock continues to grow at the same rate, how large will it be in 2020?
46. Given the formula: N (t )  N 0e kt , where N 0 is the initial amount and N(t) is the amount at time t and k is
the constant of decay. Plutonium-239 has a half-life of about 24,000 years. How much of a 100-gram quantity
of plutonium-239 will remain after 50 years?
47. The rate at which liquid vitamin breaks down in the average human body can be modeled by y  D(0.95) x ,
where y ml of the original dose D remains after x minutes. How long will it take for an original does of 15 ml
to be reduced to less than 5 ml?
Review:
48. Divide:
4x
3
 15 x 2  23x  10    x  5
49. Factor: 6 x 2  13 x  5
50. Factor: 75x 2 48 y 4
51. Factor: y 3  3 y 2  4 y  12
52. Solve the system:
2 x  3 y  11
4x  y  1
53. Solve for x: wx 2  bx  4  0
Answers:
2) log A C  B
1) An exponent
4) 4log3 M  2log3 N
3) M P  N
5) 2log5 A  3log5 B
6) 4log7  2 x  3
7) ln 7  ln x  3ln y  2 ln w
8) log3 56
W 2 
9) log  3 
P 
 A3 
10) ln  4 4 
B C 
11) 3
12) 49
13) y  1
14) 0
15) 1
16) x 
5
4
20) x 
2log 5
 9.57
 log 7  log 5
17) x  
7
log  
 3   .53
22) x 
log 5
3
5
log11
 3.46
log 2
21) x 
 log 7  4 log 3  2.08
 log 3  log 7 
23) x 
log 3
 4.92
 log 5  log 4 
24) x 
63
2
25) x  3or 4
28) x 
15
2
29) x 
31)
18) x 
26) x 
e7
 182.77
6
9  109
 .72
2
32)
1
log  
 2   2  1.37
19) x 
log 3
27) x  ln 6 1  .79
30) x  log 27  2  3.43
33)
34)
41) f 1 ( x)  e x  3
42) g 1 ( x) 
#35-38 Do Not Do Not on Test
39) f 1 ( x) 
x 8
2
40) g 1 ( x)  log x  1
5
5
log  
ln  
2
2
 14.58 years44) t     14.54 years
43) t 
.063
 .063 
12 log 1 

12 

x2
3  5x
 194 
ln 

22 

45) k 
 .0345526302 ; 22e.034552630280  349 ; So, there will be 349 whooping cranes in 2020.
63
1
ln  
2
46) k     .0000288811325 ; 100e .000028881132550  99.86 ;
24, 000
So there will 99.86 grams of Plutonium-239 left after 50 years.
1
log  
 3   21.42 minutes
47) x 
log .95 
48) 4 x 2  5 x  2
49)
3x  5 2x 1
50) 3  5 x  4 y 2  5 x  4 y 2 
51)
 y  3 y  2 y  2
52) 1, 3
53) x 
b  b2  16w
2w