Deck 4: Logarithm Functions

Question 1

Simplify
∙ ∙ ∙ Enter your answer exactly as .

Answer 1

Question 2

Simplify
∙ Enter your answer exactly as .

Answer 2

Question 3

Simplify
∙ ∙ Enter your answer exactly as .

Answer 3

∙

Question 4

Simplify
∙ ∙ Enter your answer exactly as .

Question 5

Simplify
Enter your answer exactly in the form , where P(x) is a polynomial.

Question 6

Simplify
∙ ∙ Enter your answer as .

Question 7

Simplify
Enter your answer exactly as .

Question 8

Simplify
∙ Enter your answer exactly as .

Question 9

If ∙ ∙ = , find t.

A) t =
B) t = -2
C) t =
D) t = -1

Question 10

Choose the one alternative that best completes the statement or answers the question.
( ∙ ( ∙ (

A) (
B)
C)
D) (

Question 11

Choose the one alternative that best completes the statement or answers the question.
∙ ∙

A)
B)
C) 1
D) cannot be simplified

Question 12

Simplify
∙ ∙ Enter your answer exactly as .

Question 13

Simplify
∙ ∙ ∙ Enter your answer exactly as where a is an integer.

Question 14

If = , find x.

A) x = -2
B) x = 3
C) x =
D) x =

Question 15

Choose the one alternative that best completes the statement or answers the question.
∙ ∙

A)
B)
C)
D) cannot be simplified

Question 16

Choose the one alternative that best completes the statement or answers the question.

A)
B)
C)
D) none of these

Question 17

Simplify
( Enter your answer exactly in the form where P is a polynomial.

Question 18

Simplify
∙ ∙ ∙ Enter your answer as where P is a polynomial in x in standard form.

Question 19

Choose the one alternative that best completes the statement or answers the question.
∙ ∙

A)
B)
C)
D) cannot be simplified

Question 20

Simplify
∙ ∙ Enter your answer exactly as

Question 21

Solve for x: ∙ = 64.
Enter your answer exactly as x = a (with a an integer).

Question 22

Solve for x: ∙ ∙ = .
Enter your answer exactly as x = a, b ( a < b).

Question 23

Find the equation of the tangent line to the curve y = at .
Enter your answer in slope-intercept form with any fractions reduced as .

Question 24

Solve for x: ∙ 49 ∙ ∙ = 1.
Enter your answer exactly as x = a, b (a < b).

Question 25

Find the equation of the tangent line to the curve y = at (1, e) in the simplest form.

Question 26

Simplify.
∙ ∙

A)
B)
C)
D) cannot be simplified

Question 27

The expression may be factored as shown. Find the missing factor. = 25( )Enter your answer as .

Question 28

A) t =
B) t = -
C) t =
D) t =

Question 29

Find the equation of the tangent line to the curve at (1, e) in slope-intercept form.

Question 30

Simplify.
∙ 2 ∙

A) 10
B) 10
C) 11
D) cannot be simplified

Question 31

Simplify.

A)
B)
C)
D)
E) none of these

Question 32

Simplify.

A) 5
B)
C)
D) 5

Question 33

Find the slope of the tangent line to the curve (x + at (0, 1).
Enter just an integer.

Question 34

Solve for x: ( ∙ 25 = 125 ∙ .
Enter your answer exactly as x = in lowest terms.

Question 35

Solve for x: ∙ ∙ = 25.
Enter your answer exactly as x = in lowest terms.

Question 36

If = 81, find x.

A) x = -
B) x = -3
C) x = -
D) none of these

Question 37

Find the slope of the tangent line to the curve y = at (1, e).
Enter just an integer.

Question 38

If + + = 75, find t.

A) t = 5
B) t = 25
C) t = 2
D) t cannot be determined

Question 39

The expression may be factored as shown. Find the missing factor. ( )Enter your answer as + b.

Question 40

Estimate the slope of the curve at x = 0.

A) 1
B) 0
C) e
D)
E) none of these

Question 41

If ( ∙ ∙ e = , find x.

A) -2
B) -1 or -2
C) -
D) -
Differentiate.

Question 42

f(x) = Enter your answer exactly as just where P and Q are polynomials in in standard form.

Question 43

Enter your answer exactly as just a where P is a polynomial in in standard form.

Question 44

Differentiate.

A) 3x
B)
C) 3
D)

Question 45

Simplify.
( + Enter your answer exactly as + + c (b < a).

Question 46

f(x) = Enter your answer exactly as where P and Q are polynomials.

Question 47

f(x) = Enter your answer exactly as just .

Question 48

f(x) = 4 Enter your answer exactly as just a .

Question 49

- Enter your answer exactly as a - c

Question 50

Differentiate.
(6 - x

A) 3(12 - 1
B) 3(6 - x (12 - 1)
C) 3(12 - 1
D) 3(6 - x (12 )

Question 51

f(x) = (1 + ) Enter your answer exactly in the form (P(x)) where P is a polynomial.

Question 52

f(x) = Enter your answer exactly as just (Q(x)) where P and Q are polynomials in x in standard form.

Question 53

Differentiate.

A) -
B)
C)
D) -

Question 54

Simplify.
Enter your answer exactly as where P is a polynomial with any fractions in the form in lowest terms.

Question 55

Simplify.
( + )( - )Enter your answer exactly as

Question 56

Find the first and second derivatives of f(x) = $$\frac { 1 - 2 x } { e ^ { x } }$$ .

A) f'(x) = 2x $e ^ { x }$ - 3 $e ^ { x }$ , F''(x) = 2x $e ^ { x }$ - $e ^ { x }$
B) f'(x) = 4x $e ^ { x }$ - 2 $e ^ { x }$ , F''(x) = 4x $e ^ { x }$ + 2 $e ^ { x }$
C) f'(x) = $\frac { 3 - 2 x } { e ^ { x } }$ , F''(x) = $\frac { 2 x - 5 } { e ^ { x } }$
D) f'(x) = $\frac { 2 x - 3 } { e ^ { x } }$ , F''(x) = $\frac { 5 - 2 x } { e ^ { x } }$

Question 57

Simplify.
∙ Enter your answer as .

Question 58

f(x) = + + Enter your answer exactly as just P( ) where P is a polynomial in in standard form.

Question 59

Differentiate.
(1 - 4 )

A) -8 ∙ x
B) 2x - 8x - 4
C) 2x - 8x - 4
D) -8

Question 60

Differentiate.

A) 0
B)
C)
D) 1

Question 61

Let y = . What is ?

A) 2
B)
C)
D)
E) none of these

Question 62

Simplify.
ln( - 2) + e ∙ ln( - 2)

A) (ln + 1)( - 2)
B) ln( - 2) + ( - 2)
C) ±
D) (1 + e)ln ( - 2)

Question 63

Simplify.
+ ln( ∙ )

A) 10 + x ∙
B) 29 + x
C) 25 + 4x
D) 10 + 4x

Question 64

Enter just a standard polynomial in x.

Question 65

Enter just a standard polynomial in x.

Question 66

Which of the following properties are true of the graph of y = 10 ?
(I) It is concave up.
(II) The y-intercept is (0, 2).
(III) It has a minimum at x = 0.
(IV) y is positive for x ≥ 0 and negative for x < 0.

A) I only
B) I and III
C) I and II
D) III and IV

Question 67

Determine a function y = f(x) such that y' = y and f(0) = -3?

A) y = -3
B) y = - 3
C) y = - 3
D) y =
E) none of these

Question 68

If ln x = -3.6, write x using the exponential function.

A)
B)
C) 3.6
D)

Question 69

Solve for x.
3 + ln x = 0

A) x = ln(-3)
B) x =
C) x = ln
D) x = -
E) none of these

Question 70

ln Enter your answer exactly in the form where b is an integer.

Question 71

ln Enter just a standard polynomial in x.

Question 72

If = 6, write x in terms of the natural logarithm.

A) ln 6
B) -ln 6
C) ln -6
D) 6

Question 73

Which of the following functions satisfy the differential equation y' = -8y?
(I) y = -
(II) y = + 3
(III) y = 5 (IV) y = 6

A) II and III
B) I and IV
C) II only
D) III only
E) none of these

Question 74

Enter just a standard polynomial in x.

Question 75

ln - ln Enter just a standard polynomial in x with any fractions reduced of form .

Question 76

Which of the following functions y = f(x) satisfy y'= 32y, f (0) = ?
(I) y = 32
(II) y =
(III) y = (IV) y =

A) I only
B) IV only
C) III only
D) I and II
E) none of these

Question 77

Find the values of x at which the function f(x) = $e ^ { - 2 x }$ + 2x has a possible relative maximum or minimum point.

A) maximum at x = $\frac { 0.69 } { 2 }$
B) There are no relative maximum/minimum points.
C) minimum at x = 0
D) maximum at x = $\frac { \mathrm { e } } { 2 }$
E) none of these

Question 78

Enter just a standard polynomial in x.

Question 79

Enter your answer exactly as .

Question 80

Which of the following functions y = f(x) satisfy y' = - $\frac { 2 } { 3 }$ y, f(1) = 1?
(I) y = $e ^ { x }$
(II) y = $e ^ { - 2 / 3 x }$
(III) y = $\mathrm { e } ^ { ( - 2 / 3 ) ( x - 1 ) }$ (IV) y = - $\frac { 2 } { 3 }$ $e ^ { x }$

A) III only
B) I and II
C) IV only
D) II only
E) none of these