Math 73 Practice Exam 2

1) Simplify 3!! ! !! !! 6!! ! !! ! !! !"

!! !

!
a)

!!

b)

!!

c) !!!

d) !! !

2) Simplify −4! ! ! !

!

−3! ! ! !

a) −432! !" ! !

b) −144! ! ! !

c) 432! !" ! !

d) 432! !" !!" 3) Simplify

!!!" !

!!"

!! ! !

!"! ! !

!!!

!

!!!"

!"!"

!!!

a) !!! !"

b) !!! !

c) !!! !

d) !!! !" 4) Given ! ! = ! !!! , evaluate f(2). a) 0.2707

b) .0183

c) .2708

d) .0184 5) Given ! ! = 2!!! , evaluate f(5). a) 16

b) ¼

c) 8

d) 4

!

6) The graph of ! ! = ! 2.2 !

a)
b)
c)
d)

goes up to the right, and goes through (0, 2.2) goes up to the left, and goes through (1, 2.2) goes up to the right, and goes through (0, 0.5) goes up to the left, and goes through (0, 2.2)

7) Find the equation of the exponential that goes through (-­‐1, 1/2) and (0, 1). !

a) ! = ! 0.5 !

b) ! = 2!

c) ! =

! !
!

!

d) ! = ! 1 !

8) Find the equation of the exponential that goes through (-­‐2, 2/3) and (2, 19). a) ! = 8!

b) ! = 4 2 !

c) ! = 3.56 2.31 !

d) ! = 3.5 . 67 !

!
9) Let ! ! = ! ! − 2. Find ! !! ! .

!
!
!!
a)

! ! = ! ! + 4

b) ! !! ! = !!!

c) ! !! ! = 2! + 2 d) ! !! ! = 2! + 4

10)Which of the functions are inverses of each other?

a) ! ! = 3! , ! ! = −3!

b)

! ! = 2! − 7 , ! ! = −2! + 7

!
!
!
c)

! ! = 4! − 1, ! ! = ! + !

d)

! ! = −2! + 1 , ! ! = − ! ! − 1

11)Find the inverse of the function 2,1 , −3,5 , 6, −7

a) 2,1 , 3, −5 , 6, −7

b) { 1,2 , 5, −3 , −7,6 }

!
! !
!
!
c)

{ ! , −1 , − ! , ! , ! , − ! }

d)

{ −2, −1 , 3, −5 , −6, 7 }

12)Write log !

!!!
!!

in expanded form:

!
!
!
a)

log ! ! + ! log ! ! − 3 log ! !

b) ! log ! ! + ! log ! ! − 3 log ! !

!
c)

log ! ! − ! log ! ! + 3 log ! !

c) ! ! (log ! ! ! !)

!
13)Write
! 2 log ! ! − 4 log ! ! as a single logarithm with a coefficient of 1:

a) log !

!

! ! ! !

b) log !

!

!!
!!

!

c) (log ! ! ! )/(log !

!

! ! ) d) log !

14)Evaluate log ! 60. Round to the nearest ten-­‐thousandth.

a) 2.0476

b) 1.0133

c) 1.9690

d) 0.9640

15)Solve for x: 16!!!! = 64!!!

a) 13/5

b)

1

c) 13/11

d) 3

!

!!
!!