Free Printable Precalc Final Review 1: Exponential and Logarithmic Equation

1.

Solve for the value of x.

1100 = 11x²

a)

x=100

b)

x=5

c)

x=11

d)

x=10

2.

Solve for the value of x.

500 = 4x³

a)

x=3

b)

x=5

c)

x=2

d)

x=125

3.

Write an exponential function in the form y=ab^x that goes through points (0,13) and (5,416).

a)

y=13(32)^x

b)

y=13(2)^x

c)

y=13(5)^x

d)

y=2(13)^x

4.

Write an exponential function in the form y=ab^x that goes through points (0,4) and (2,324).

a)

y=4(9)^x

b)

y=9(4)^x

c)

y=2(4)^x

d)

y=4(81)^x

5.

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3,72).

a)

y=9(3)^x

b)

y=2(9)^x

c)

y=9(2)^x

d)

y=8(3)^x

6.

Write an exponential function in the form y=ab^x that goes through points (0,10) and (2,160).

a)

y=10(2)^x

b)

y=4(10)^x

c)

y=16(4)^x

d)

y=10(4)^x

7.

Which equation describes the story below?

You start with $5 and triple your money every day.

a)

y=5(3)^x

b)

y=5^x

c)

y=5(3x)

d)

y=15^x

8.

Write an exponential function to model the situation. Then solve.

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

a)

C(t) = 12000(1.06)^t ; $3149.72

b)

C(t) = 12000(.06)^t ; $3149.72

c)

C(t) = 12000(.06)^t ; $1472.95

d)

C(t) = 12000(1.06)^t ; $15149.72

9.

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 6 of these cells?

a)

f(h) = 3(6)^h

b)

f(h) = 6x^h

c)

f(h) = 6(3)^h

d)

f(h) = 3(6h)

10.

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.

Which function models the amount of cola in gallons after h hours?

a)

f(h) = 75(-5)^h

b)

f(h) = -5(75)^h

c)

f(h) = .95(75)^h

d)

f(h) = 75(.95)^h

11.

The function y = 24,220 (0.85)^x represents Mr. Bittle's investment in the stock exchange where x is measured in months.

Which statement is NOT true.

a)

Mr. Bittle loses 85% of his investment monthly

b)

Mr. Bittle initially invested $24,220

c)

Each month Mr. Bittle loses 15% of his investment

12.

What is the a-value (or y-intercept) for the function: f(x) = 800(0.85)^x?

a)

800

b)

0.85

c)

0.15

d)

x

13.

What is the decay rate for the function: f(x) = 800(0.85)^x?

a)

800

b)

0.85

c)

15%

d)

x

14.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^0.08

b)

^1.08

c)

0.92

d)

8

15.

Write an exponential function to model the situation. Then solve.

The value of a car is $18000 and is depreciating at a rate of 12% per year. What will the value of the car be after 10 years?

a)

V(t) = 18000(.88)^t ; $12986.98

b)

V(t) = 18000(.12)^t ; $12986.98

c)

V(t) = 18000(.88)^t ; $5013.02

d)

V(t) = 18000(.12)^t ; $5013.02

16.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

17.

Determine if the equation y = 15(1.35)^x represents exponential growth or decay and justify. Hint: Think about the growth and decay equations.

a)

Growth, because the scale factor is greater than 1

b)

Growth, because the scale factor is less than 1

c)

Decay, because the scale factor is greater than 1

d)

Decay, because the scale factor is less than 1

18.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

19.

The equation f(x) = 300(1.06)^x is being used to calculate the amount of money in a savings account. What does the 1.06 represent?

a)

6% growth

b)

6% decay

c)

1.06% growth

d)

.06% decay

20.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation that models this situation?

a)

y = 8(15,000)^x

b)

y = 15,000(1.08)^x

c)

y = 15,000(0.92)^x

d)

y = 15,000(0.08)^x

21.

Write an exponential function in the form y=ab^x that goes through points (0,13) and (2,325).

a)

y=13(5)^x

b)

y=13(2)^x

c)

y=5(13)^x

d)

y=2(5)^x

22.

Write an exponential function in the form y=ab^x that goes through points (0,15) and (2,240).

a)

y=2(15)^x

b)

y=2(4)^x

c)

y=4(15)^x

d)

y=15(4)^x

23.

Write an exponential function in the form y=ab^x that goes through points (0,2) and (3,128).

a)

y=2(3)^x

b)

y=2(4)^x

c)

y=3(4)^x

d)

y=4(2)^x

24.

Write an exponential function in the form y=ab^x that goes through points (0,18) and (2,288).

a)

y=18(4)^x

b)

y=4(2)^x

c)

y=4(18)^x

d)

y=2(4)^x

25.

Write an exponential function in the form y=ab^x that goes through points (0,6) and (2,96).

a)

y=6(2)^x

b)

y=2(4)^x

c)

y=4(6)^x

d)

y=6(4)^x

26.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

27.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

28.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

29.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

30.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

31.

81^3-x = (1/3)^5x-6

a)

6

b)

-6

c)

9/2

d)

3/2

32.

Solve the following exponential equation:

3^3=3^{4x+2}

a)

$x=\frac{1}{4}$

b)

$x=-\frac{1}{4}$

c)

$x=\frac{1}{2}$

d)

$x=-\frac{1}{2}$

33.

How would you solve an exponential equation like the one below:
$4^{2x-3}=4^{6x+5}$

a)

Rewrite $4$ as $2^2$

b)

Multiply the exponents

c)

Set the exponents equal to each other

d)

Add the exponents

34.

How would you solve an exponential equation like the one below:
$3^{x+7}=27^{-3x-1}$

a)

Rewrite $27$ as $3^3$

b)

Multiply the exponents

c)

Set the exponents equal to each other

d)

Add the exponents

35.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

36.

Solve for x

a)

1.641

b)

1.825

c)

1.709

d)

1.908

37.

Solve for x

a)

-0.659

b)

-0.528

c)

-2.159

d)

-0.478

38.

solve for x.

$8^{-x}=2^{5x}\cdot4^{3x+1}$

a)

-1/15

b)

-1/18

c)

-1/9

d)

-1/7

39.

Solve the following exponential equation.

$9^{8-x}=27^{x-3}$

a)

$x=5$

b)

$x=-5$

c)

$x=\frac{1}{5}$

d)

$x=-\frac{1}{5}$

40.

Solve for x:
8^x+1= 3

a)

0.528

b)

0.893

c)

-0.472

d)

1.893

41.

Solve for x:
4^x- 5 = 12

a)

0.489

b)

2.552

c)

0.893

d)

2.044

42.

Solve for x.
e^x+6 + 5 = 1

a)

-4.614

b)

-4.236

c)

No Solution

d)

-0.334

43.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

44.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

45.

Write 2³= 8 in logarithmic form.

a)

log₂ 8 = 3

b)

log₂ 3 = 8

c)

log₃ 8 = 2

d)

log₃ 2 = 8

46.

Write 10⁴= 10000 in logarithmic form.

a)

log₁₀ 4 = 10000

b)

log₁₀₀₀₀ 4 = 10

c)

log₁₀ 10000 = 4

d)

log₄ 10000 = 10

47.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

48.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

49.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

50.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

51.

Write log₃ 81 = 4 in exponential form.

a)

81⁴=3

b)

81³=4

c)

4³=81

d)

3⁴=81

52.

Write log₆ 216 = 3 in exponential form.

a)

3⁶=216

b)

6³=216

c)

216⁶=3

d)

3²¹⁶=6

53.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

54.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

55.

Evaluate log₈ 8

a)

8

b)

-1

c)

0

d)

1

56.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

57.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

58.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

59.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

60.

Evaluate Log 100

a)

2

b)

3

c)

$\frac{1}{10}$

d)

100

61.

Evaluate Log $\frac{1}{100}$

a)

2

b)

3

c)

$\frac{1}{10}$

d)

-2

62.

Evaluate Log 25 to 2 decimal spaces

a)

5.25

b)

1.25

c)

1.40

d)

3.85

63.

Evaluate Log 4 to 2 decimal spaces

a)

2.00

b)

0.60

c)

1.40

d)

0.25

64.

Condense this expression to a single logarithm.

a)

b)

c)

d)

65.

Condense this expression to a single logarithm.

a)

b)

c)

d)

66.

Condense this expression to a single logarithm.

a)

b)

c)

d)

67.

Condense this expression to a single logarithm.

a)

b)

c)

d)

68.

$\log_312$
Which of the following is a possible expansion for this logarithm? Check all that apply.

a)

$\log_34+\log_33$

b)

$\log_310+\log_32$

c)

$\log_32+\log_36$

d)

$\log_336-\log_33$

e)

$\log_315-\log_33$

69.

$\log_312$
Which of the following is a possible expansion for this logarithm? Check all that apply.

a)

$\log_34+\log_33$

b)

$\log_310+\log_32$

c)

$\log_32+\log_36$

d)

$\log_336-\log_33$

e)

$\log_315-\log_33$

70.

$\log_324$
Which of the following is a possible expansion for this logarithm? Check all that apply.

a)

$\log_34+\log_320$

b)

$\log_310+\log_314$

c)

$\log_34+\log_36$

d)

$\log_348-\log_32$

e)

$\log_38+\log_33$

71.

$3\log_45$

Condense into a single logarithm. Simplify if possible.

a)

$\log_415$

b)

$\log_4125$

c)

$\log_43^5$

d)

$\log_{ }60$

72.

$5\log_{9\ }x$

Condense into a single logarithm. Simplify if possible.

a)

$\log45x$

b)

$\log_95x$

c)

$\log_9x^5$

d)

$\log_{ }14x$

73.

$\frac{1}{2}\log_{4\ }9$

Condense into a single logarithm. Simplify if possible.

a)

$\log18$

b)

$\log_4\ \frac{9}{2}$

c)

$\log_44.5$

d)

$\log_43$

74.

$\log_{3\ }4^8$

Expand using the product property. Simplify if possible.

a)

$8\log_34$

b)

$4\log_38$

c)

$3\log_84$

d)

$8\log_43$

75.

Condense this expression into a single logarithm.

a)

b)

c)

d)

76.

A log with a base of 10 is known as the (a) log.

77.

Condense this expression into a single logarithm.

a)

b)

c)

d)

78.

Expand this logarithm.

a)

b)

c)

d)

79.

Expand this logarithm.

a)

b)

c)

d)

80.

Expand this logarithm.

a)

b)

c)

d)

81.

Expand this logarithm.

a)

b)

c)

d)

82.

Condense this expression into a single logarithm.

a)

b)

c)

d)

83.

Condense this expression into a single logarithm.

a)

b)

c)

d)

Precalc Final Review 1: Exponential and Logarithmic Equation

Total questions: 83

Worksheet time: 2hrs 7mins

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