Free Printable H.W2 G11 STS

Worksheets

H.W2 G11 STS

Total questions: 55

Worksheet time: 2hrs 19mins

Name

Class

Date

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

-1

Evaluate.
log₃81

¹/₄

-4

-¹/₄

Evaluate.
3 log₂4

Solve:
_{log (4x − 5) = log (2x − 1)}

4^(x-2)= 64^(x+1)

-2/5

-5/2

7/2

2/7

Evaluate without a calculator:

log_1/44

-1

-4

Evaluate without a calculator:

log0.001

1/1000

1/10,000

-2

-3

Evaluate without a calculator:

ln(1/e)

-1

-e

Evaluate without a calculator:

log_1/2(1/64)

1/32

-1/32

-6

10.

Which of the following is the correct exponential form of log (0.001) = -3?

10^0.001 = -3

e^-3 = 0.001

-3¹⁰ = 0.001

10^-3 = 0.001

11.

Which of the following is the logarithmic form of the given equation?

12.

Condense, then simplify if possible.
log 6 - log 3 + 2 log 7

log 98

log 78

log 56

log 45

13.

Condense.
6 log₆ x + 2 log₆y

14.

Which of the following illustrates the Product Property of Logarithms

log₃(x) ⋅ log₃(y) = log₃(x+y)

log₃(x) ⋅ log₃(y) = log₃(xy)

log₃(x) + log₃(y) = log₃(xy)

15.

Which of the following illustrates the Power Property of Logarithms

log₅(m)ⁿ = n + log₅(m)

log₅(m)ⁿ = n ⋅ log₅(m)

log₅(m)ⁿ = log₅(n ⋅ m)

16.

Expand the logarithm: log₂∛(xyz)

(1/3) (log₂(x + y + z)

(1/3) log₂(x) - (1/3) log₂(y) - (1/3) log₂(z)

(1/3) log₂(x) + (1/3) log₂(y) + (1/3) log₂(z)

(1/3) log₂(x) + log₂(y) + log₂(z)

17.

Expand the logarithm: ln(x ÷ y²)⁴

4ln(x) ÷ 8ln(y)

4ln(x) − 4ln(y)

4ln(x − y²)

4ln(x) − 8ln(y)

18.

Solve:
log (4p - 2) = log (-5p + 5)

p = 9/7

p = -7/9

p = -7

p = 7/9

19.

Solve:
10^{2 - 2b} = 60

x = .1109

x = -29

x = 2.7782

x = -.8817

20.

State the property (s) used to simplify the expression

log₄20 - 3log₄x = log₄(20/x³)

Power Property

Quotient Property

Quotient and Power Property

Product and Power Property

21.

Write the logarithm expression as a single logarithm

2log 4 + log 2

log 8

log 16

log 32

log 8²

22.

Which equation best describes the graph?

y = 2^x + 4

y = 2^x - 3

y = 2^x - 4

y = 2^x + 3

23.

Match the graph with its equation

y = log₆(-x) + 1

y = log₆(x − 2) + 1

y = log₆(x + 2) - 1

y = log(x-8) + 1

24.

Match the graph with its equation

y = log₅ (x + 1) + 1

y = log₅ (x - 1) + 1

y = log₅ (x²) + 1

y = log₅ (x)-1

25.

Match the graph with its equation

y = log₄ (x)+2

y = log₄ (x + 2) + 1

y = log₄ (x - 1) + 2

y = log₄ (-x + 2)

26.

27.

What is the asymptote of this function:
f(x) = 2^x-1+ 3

x = 1

x = -1

y = 3

y = - 3

28.

What is the range of log(x)?

(-2, 4)

(-∞, ∞)

(-∞, 0)

Cucumber

29.

What is the domain of log(x)?

(-∞, ∞)

[0, ∞)

(0, ∞)

Pickle

30.

Using the parent function y=3^x what would the graph of y=3^x+1 look like?

Horizontal shift left one unit

Horizontal shift right one unit

Vertical shift up one unit

Vertical shift down one unit

31.

What is the Asymptote?

x=5

x=0

y=0

x=1

32.

What is the equation of the asymptote?

x = -3

x=5

y= -3

y=5

33.

Which has a horizontal asymptote?

Exponential

Logarithmic

Both

34.

Which has a vertical asymptote?

Exponential

Logarithmic

Both

35.

What is the domain?

(-∞, ∞)

(0, ∞)

[1, ∞)

(1, ∞)

36.

As x --> 1, f(x) --> ____

∞

-∞

37.

What is the Range (all possible outputs) of f(x)=2^x+1-3

All real

(-∞,-3)

(-3,

∞)

(-1,

∞)

38.

Find the domain (all possible inputs) of -ln(x-2)+3

all real

(-∞,2)

(-∞,3)

(2,∞)

39.

Find the asymptote of -ln(x-2)+3

x=2

x=3

y=2

y=3

40.

Which has the point (1,0) in the parent function?

exponential

logarithm

both

41.

Which equation matches the graph?

y = -(2)^x+2-3

y = 2^x+3-2

y = -(2)^x-2-3

y = -(2)^x+1-2

42.

Given g(x)=5^x
Write a function that is reflected over the line x-axis and translated 4 units to the right.

f(x)= -5^x-4

f(x)= -5^x+4

f(x)= 5⁽^x-4)

f(x)= 5^-(x-4)

43.

Solve the following equation. Round your solution to two decimal places.
4 - 3 ln(2x + 10) = 12

x = 2.20

x = 1.68

x = -5.00

x = -4.97

44.

log (x - 1) - log (x - 2) = log 5

4/9

9/4

1/7

45.

ln(4-v) = ln(3v)

-2

No Solution

-5

46.

Solve log(x) + log(x+3) = 1

-2

-5

47.

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

"e"

Natural Logarithm (LN)

Common Logarithm (Log)

Natural Log, base "e"
LN_e

48.

(2e+2)/3

(2e-2)/3

(3e-2)/2

49.

log₂(x²- 6) = log₂(2x+2)

4, -2

No Solution

-2

50.

log₂(x + 2) + log₂x = 3

-4, 2

-2, 4

51.

Solve.
ln√(x+3)=4

e²-3

e⁴-3

e⁸-3

e⁸+3

52.

Solve.
e^4x=12

2.48

9.94

0.62

53.

Solve for x.
e^2x-e^x-2 = 0

x = 0

x = ln 2, ln -1

x = ln 2, ln 0

x = ln2

54.

How much money would need to be invested today if you want $40,000 in 18 years at 4.5% if compounded continuously.

$19,923.22

$17,794.32

$89,916.32

$1 Bob

55.

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)

1 year

242 years

20 years

13 years

Reset

H.W2 G11 STS

Total questions: 55

Worksheet time: 2hrs 19mins

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