Pre-Calculus Honors
Part I
log3 1  log3 4 log3 9  log3 2
1. If A 
, then 3A 
log3 1  log3 9 log3 8  log3 4 
A.
1
3
B.
81
16
C.
Unit 9 Review
No Calculator
1
9
D. 1
E.
9
2
2. Which of the following represents the sum of the y-values of the points of intersection of the graphs of
y  log6 x2 and y  log6  x  6  ?
A. 2
B. log6 12
C. 1
D. log6 9

3. Find the value(s) of x that satisfy the equation log x  log  x  2  log x 2  2x
A. x < 0
B. 0 < x < 2
C. x > 2
D.
4. If a  log8 16 and b  log16 5, which of the following is equivalent to
A. log6 5
B. log5
C. log8 5
E. 0

 ,  
3ab
?
3ab  1
D. log5 8
E. 
E. log5 6
5. If log log A   logB  log logC , where A, B, C >1, find A in terms of B and C.
A. A  C B
B. A  10logB C
C. A  B C


6. How many integer solutions satisfy the inequality ln log4 x2  5
A. 0
B. 1
7. Given x > 1 and logx x x  logx x 5x  logx
2
A. -6, 1
B. 2, 3
D. A  10logC B
E. A 
D. 4
E. 5
logB
logC
  0 ?
C. 2
1
, find all values of x that satisfy the equation.
x6
C. 4
D. 1, 6
E. -1, 6
8. Solve for y, given that y > 2 and sin x > 0: ln  y  2  ln  sin x   3x
A. e3x sin x  2
9. Given that
A. 21
10.
B. e3x sin x  2
11. Given that a2b  5, find 2a6b  4
A. 24
B. 240
A.
1
2
E. e3x sin x  2
D. 441
E. 576
C. 3
D. 4
E. 5
C. 246
D. 996
E. 2010
1
1

 x , find the value of 4 x
log7 2 log9 4
B. 24
C. 128
1
1
5



log4 18 2log6 3  log6 2 log3 18
A. 1
B. 2
12. If y  logb
D. e3x sin x  2
C. e3x sin x  2
1  1  x2
, where 0 < x < 1, b > 0, and b  1, which of the following represents the value of y 1  0  ?
x
B. 1
C. 2
D. y 1  0  is undefined E. -1
For 13-15,
a) State the domain and range of the function.
b) Find the inverse of the function if possible.
c) Find the domain and range of the inverse (if it exists)
13. f  x  
2x  3
5x  2
14. f  x  
3
x1/3
15. f  x   x  2
For 16-18, write each expression as the sum and/or difference of logarithms with no exponents.
uv
16. log3 3
w

17. ln x

x 1
2
3
 2x  3 
18. ln  2

 x  3x  2 
2
For 19-21, find y as a function of x. The constant C is a positive number.
19. ln y  2x 2  C
20. ln  y  3   ln  y  3   x  C
21. ey C  x2  4
For 22- 30, solve each equation for x.
1
2
x2  2
22. 863x  4
23. 4 x  x 
24. log
25. 92x  273x 4
26. log3
27. e1 x  5
28. log6  x  3   log6  x  4   1
2
29. log  7x  12  2log x
Pre-Calculus Honors
Part II
2
x  6
30. 2x 18 x  4
Unit 9 Review
Calculator Required
31. The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the
log s  logi
formula n 
where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of
log 1  d
depreciation.
a. How many years will it take for a piece of machinery to decline in value from $90,000 to $10,000 if the annual rate
of depreciation is 20%?
b. How many years will it take for a piece of machinery to lose halve of its value if the annual rate of depreciation is
15%?
0.8
represents the proportion of new computers sold that utilize the
1  1.67e0.16t
Microsoft Windows 7 operating system. Let t = 0 represent 2011, t = 1 represent 2012, etc.
32. The logistic growth model P  t  
a. What percent of new computers sold in 2011 utilize Windows 7?
b. Determine the maximum percentage of new computers sold that will utilize Windows 7.
c. During which month and year will 75% of the new computers sold utilize Windows 7?
33. A telescope is limited in its usefulness by the brightness of the star it is aimed at and by the diameter of its lens. One
measure of a star’s brightness is its magnitude: the dimmer the star, the larger its magnitude. A formula for the
limiting magnitude L of a telescope, that is, the magnitude of the dimmest star that it can be used to view, is given by
L  9  5.1logd where d is the diameter (in inches) of the lens.
a. What is the limiting magnitude of a 3.5 inch telescope?
b. What diameter is required to view a star of magnitude 14?