1. Exponentials, Logarithms, and Inverses
Created by Educational Technology Network

2. Exponential Functions
Logarithm Functions
Hodgepodge
Inverses (Algebra)
Inverses (Graphs)
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3. Exponentials – 100 Points
QUESTION:
(30 sec.) Simplify
ANSWER:
7v5/2

4. Exponentials – 200 Points QUESTION: ANSWER:
(1 min) Convert to a logarithm: 36=729
ANSWER:
Log3729 = 6

5. Exponentials – 300 Points QUESTION: ANSWER:
(1 min) Simplify the following:
3x/3y 3x•3y (3x)y
ANSWER:
3x-y 3x+y 3x•y

6. Exponentials – 400 Points QUESTION: ANSWER: (2 min) Solve: 5(67x)=13

7. Exponentials – 500 Points QUESTION: ANSWER:
(4 min) Solve: e2x – 6ex +8 = 0 (Hint: factor)
ANSWER:
ex = 2  x =
ex = 4  x =

8. Logarithms– 100 Points QUESTION: ANSWER:
(2 min) Expand the following: Log2 √(2x(x2+2))
ANSWER:
½ • [Log22+Log2x+Log2(x2+2)]

9. Logarithms – 200 Points QUESTION: ANSWER:
(2 min) Write the expression as a single logarithm
3 ln 2 – ½ ln x + ln (x+1)
ANSWER:
ln [ (8•(x+1) ) / ( √(x) ) ]

10. Logarithms – 300 Points QUESTION: ANSWER:
List the Product, Quotient and Power of a Power Logarithm properties. (1 min)
ANSWER:
Product: Logb(mn) = Logbm + Logbn
Quotient: Logb(m/n) = Logbm – Logbn
Power: Logbmn = n•Logbm

11. Logarithms – 400 Points QUESTION: ANSWER:
(1 min)What is the change of base formula
ANSWER:
Logba = Log (a) / Log (b)

12. Logarithms – 500 Points QUESTION: ANSWER: (4 minutes) Solve for x:
log3 (x+9) = log3((x-3)/(x+2))
x+9=(x-3)/(x+2)
(x+9)(x+2) = x-3
x2+11x+18= x-3
x2+10x+21=0
(x+3) (x+7) = 0
x = -3, -7

13. Hodgepodge – 100 Points QUESTION: ANSWER:
(2 min) Expand: Log ( (7xy5) / (√(x-2) ) )
ANSWER:
Log 7 + Log x + 5•Log y + ½ Log (x-2)

14. Hodgepodge – 200 Points QUESTION: ANSWER:
(1 min) What is the base of our general Log? What about ln?
ANSWER:
Log is base 10 unless specified
Ln is the natural logarithm with a base of e

15. Hodgepodge – 300 Points QUESTION: ANSWER:
Explain using properties why taking the natural log of e7x gives you 7x
ANSWER:
Ln (e7x) = 7x •Log (e) = 7x • 1 = 7x

16. Hodgepodge – 400 Points QUESTION: ANSWER:
What mathematician was born on Pi Day?
ANSWER:
Albert Einstein

17. Hodgepodge – 500 Points QUESTION: ANSWER: Simplify and solve
x = ±1 does -1 make sense?

18. Inverses (Algebra) – 100 Points
QUESTION:
Find the inverse of f(x)=3x+2.
ANSWER:
f -1(x)=(x-2)/3

19. Inverses (Algebra) – 200 Points
QUESTION:
If regular gasoline is selling for $3.95 per gallon, the price of any particular purchase p is a function of the number of gallons g in that purchase.
Write this as a function and find its inverse
ANSWER:
Function: p=3.95•g
Inverse: g=p/3.95

20. Inverses (Algebra) – 300 Points
QUESTION:
ANSWER:
y=(7/x)-4

21. Inverses (Algebra) – 400 Points
QUESTION:
Write out the steps for either of the two algebra styles we have learned to determine the inverse of a function
ANSWER:
Answers may vary

22. Inverses (Algebra) – 500 Points
QUESTION:
How could you use composition of functions to check that f(x) and g(x) are inverses of each other?
ANSWER:
Test f(g(x)) and/or g(f(x)) and check that they equal x.

23. Inverses (Graph) – 100 Points
QUESTION:
What is the line of symmetry for functions and their inverse?
ANSWER:
y=x

24. Inverses (Graph) – 200 Points
QUESTION:
Graph the following function then graph its inverse:
y=3x+1
ANSWER:
Inverse equation: y=(x-1)/3

25. Inverses (Graph) – 300 Points
QUESTION:
Given the following functions, which have inverses that are functions? If it does not have one explain why.
a) b) c)
ANSWER:
a & b have inverse functions, c does not because it fails the “horizontal line test”

26. Inverses (Graph) – 400 Points
QUESTION:
How do the domain and range of a function relate to the domain and range of its inverse
ANSWER:
They are switched, why?

27. Inverses (Graph) – 500 Points
QUESTION:
How could I use a graph to check that my functions are inverses of each other?
ANSWER:
y=x is the line of symmetry, this is made clear when the coordinates flip (x,y)  (y,x)