Free Printable 2.8 - 2.14 Review

1.

log₅(4x-7)=log₅(x+5)

a)

3

b)

12

c)

4

d)

7

2.

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

3.

log(2x) - log(5) = log(30)

a)

6/5

b)

45/2

c)

75

d)

-3/8

4.

log₂(x²- 6) = log₂(2x+2)

a)

4, -2

b)

No Solution

c)

4

d)

-2

5.

Solve

a)

A

b)

B

c)

C

d)

D

6.

4^{3x + 5} = 16

a)

-5/3

b)

-1

c)

-3/2

d)

2/3

7.

Solve log₂ (2 - 2x) + log₂ (1 - x) = 5

a)

4

b)

5

c)

-2

d)

-3

8.

Solve for x:
3^2x = 27

a)

3/2

b)

-2

c)

0

d)

5

9.

Solve for p:
4^p+2 = 64

a)

-16/9

b)

1

c)

8

d)

7/6

10.

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

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

11.

64^4x-8 < 256^2x+6

a)

x < 12

b)

x < 7

c)

x > 3

d)

x < 0

12.

$3^{\left(x-4\right)}\ <\ \frac{1}{27}$

a)

x < 1

b)

x > -1

c)

x < 7

d)

x > 7

13.

a)

A

b)

B

c)

C

d)

D

14.

Solve each inequality.
$\log_7\left(x+2\right)\ge\log_7\left(6x\ -3\right)$

a)

$x\ \le1$

b)

$x\ >\ -2$

c)

$\frac{1}{2}\ <x\ \le1$

d)

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

15.

Expand

a)

6log₈v-2log₈u

b)

6log₈u-2log₈v

c)

3log₈u-2log₈v

d)

6log₈u+2log₈v

16.

Condense

a)

logxyz³

b)

log(xy/z³)

c)

logx+logy+logz³

d)

logx³y³z³

17.

Expand

a)

4log₄u - 16log₄v

b)

4logu + 16logv

c)

4logu - 4logv

d)

4logu / 16logv

18.

Which expression is equivalent to:

$\frac{1}{2}\ln\left(a\right)+\frac{1}{2}\ln\left(b\right)$

a)

$\ln\left(ab\right)^2$

b)

$\ln\left(ab^{\frac{1}{2}}\right)$

c)

$\ln\left(\sqrt{ab}\right)$

d)

$\ln\left(a^{\frac{1}{2}}b\right)$

19.

Condense the following expression into a single logarithm:
$2\log\left(a\right)+4\log\left(b\right)-9\log\left(c\right)$

a)

$\log\left(a^2b^4c^9\right)$

b)

$\log\left(a^2+b^4-c^9\right)$

c)

$\log\left(\frac{a^2b^4}{c^9}\right)$

d)

$\log\left(\frac{a^2}{b^4c^9}\right)$

20.

What type of function does this table represent?

a)

Linear

b)

Exponential

c)

Neither

21.

What type of function does this table represent?

a)

Linear

b)

Exponential

c)

Neither

22.

find the asymptote: y = log₁₀ (x+3)

a)

x=-3

b)

x=3

c)

y=-3

d)

y=3

23.

Match the graph with its equation

a)

y = log₄ (x)+2

b)

y = log₄ (x + 2) + 1

c)

y = log₄ (x - 1) + 2

d)

y = log₄ (-x + 2)

24.

Find the inverse of the function f(x)=5^(x+2)

a)

f^-1(x)=log₅(x-2)

b)

f^-1(x)=log₅(x)-2

c)

f^-1(x)=log₅(x)+2

d)

f^-1(x)=log₅(x+2)

25.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

26.

What is the domain and range of
f(x) = log ₃ (x + 1)?

a)

D: (− ∞, ∞) R: (−1, ∞)

b)

D: (− ∞, ∞) R: (1, ∞)

c)

D: (−1, ∞) R: (− ∞, ∞)

d)

D: (1, ∞) R: (− ∞, ∞)

27.

What are the transformations of this graph?

a)

Right 1 Up 5

b)

Right 1 Down 5

c)

Left 1 Up 5

d)

Left 1 Down 5

28.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

29.

What is the horizontal asymptote for the graph of

f(x)=13(0.5)^x?

a)

y=0.5

b)

y=13

c)

y=6

d)

y=0

30.

Identify the y-intercept of the graph of the exponential function:

y=3\left(\frac{1}{2}\right)^x

a)

(3,0)

b)

(1/2, 0)

c)

(0,0)

d)

(0,3)

31.

Describe the transformation on

y=2\left(4\right)^x

when if becomes

y=2\left(4\right)^{\left(x-5\right)}

a)

Down 5

b)

Right 5

c)

Left 5

d)

Up 5

32.

Identify the horizontal asymptote for the exponential function: $y=\frac{1}{4}\left(3\right)^x-9$

a)

y = 0

b)

y = 3

c)

y = -9

d)

No Horizonal Asymptote

33.

$y=5\left(\frac{1}{3}\right)^{\left(x-1\right)}$

Identify the horizontal asymptote for the exponential function:

a)

y = 0

b)

x = -1

c)

y = -1

d)

y = 1

34.

$y=8\left(\frac{1}{2}\right)^{\left(x-3\right)}+5$

Identify the range of the exponential function.

a)

y > -3

b)

y > 5

c)

y < 5

d)

y > -5

35.

Which equation matches this graph?

a)

b)

c)

d)

36.

Find the logarithmic regression equation (y = a+blnx) of the following data:

a)

y = 188.19 (1.02)^x

b)

y = 176.25 + 26.11ln(x)

c)

y = 188.03 + 4.51x

d)

y = -190.78 + 36.73ln(x)

37.

What is the equation of the horizontal asymptote of the function

y = 2(0.3)^{x - 1} - 4?

a)

y = -4

b)

y = 2

c)

y = 0.3

d)

y = 4

38.

What is the Equation that matches this data set?

a)

$f\left(x\right)=\left(3.73\right)\left(1.03\right)^x$

b)

$f\left(x\right)=\left(0.7\right)\left(3\right)^x$

c)

$f\left(x\right)=\left(1.03\right)\left(3.73\right)^x$

d)

$f\left(x\right)=3.73x+1.03$

39.

Write an logarithmic equation for the above table of data.

a)

y = 19.28+17.66ln(x)

b)

y = 19.28(17.66)^x

c)

y = 17.66+19.28ln(x)

d)

y = 19.28(17.66)^x

40.

What was the acronym for Residual = Actual - Predicted

a)

RAP

b)

Rest and Play

c)

Report All People

d)

Run And Play

41.

Find the inverse:

g\left(x\right)=\frac{x+5}{3}

a)

$g\left(x\right)=3x-5$

b)

$g^{-1}\left(x\right)=3x-5$

c)

$g^{-1}\left(x\right)=3x+5$

d)

$g^{-1}\left(x\right)=5x-3$

42.

Find the inverse:

g\left(x\right)=\frac{x+7}{x-3}

a)

$g^{-1}\left(x\right)=3x+7$

b)

$g^{-1}\left(x\right)=\frac{3x+7}{x-1}$

c)

$g^{-1}\left(x\right)=\frac{-7x-3}{x-1}$

d)

$g^{-1}\left(x\right)=\frac{-3x-7}{x-1}$

43.

Find the inverse:
$f\left(x\right)=\frac{15+x}{x-4}$

a)

$f^{-1}\left(x\right)=\frac{15-4x}{x+1}$

b)

$f^{-1}\left(x\right)=\frac{15-4x}{x-1}$

c)

$f^{-1}\left(x\right)=\frac{4x+15}{x+1}$

d)

$f^{-1}\left(x\right)=\frac{x+4}{x-15}$

44.

Find the Inverse.

a)

a

b)

b

c)

c

d)

d

45.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

46.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

47.

If the domain of y=h(x) is [-5,4] and its range is [-4,1], what is the domain of $y=h^{-1}\left(x\right)$ ?

a)

[4,-5]

b)

[5,-4]

c)

[-4,1]

d)

[4,-1]

48.

$f\left(x\right)=2^x+4$ , then $f^{-1}\left(20\right)=$

a)

5

b)

20

c)

4

d)

16

49.

What is the End behavior on the right side

a)

x→∞, y→∞

b)

x→⁻∞, y→∞

c)

x→⁻∞, y→0

d)

x→∞, y→⁻∞

50.

What is the End behavior on the left side

a)

x→∞, y→∞

b)

x→⁻∞, y→∞

c)

x→⁻∞, y→0

d)

x→∞, y→⁻∞

51.

What is the equation of the asymptote on the graph of $y=\log_5\left(x+3\right)+5$ ?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

52.

As x → -∞ , f(x) →

a)

-4

b)

-3

c)

∞

d)

-∞

53.

What is the end behavior of the function $y=7\left(6\right)^{x+2}+1$

a)

$x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$

b)

$x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow\infty$ $x\rightarrow\infty\ as\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow1$ $x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$

d)

$x\rightarrow1\ as\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$

54.

Without using a calculator, give the value of the following logarithm.

$\log_{ }10^{21.8}$

(a)

55.

Use a calculator to find the common logarithm. (Round to four decimal places as needed).

log(86)

(a)

56.

Use a calculator to find the common logarithm. (round to four decimal places as needed.)

log(55.8)

(a)

57.

Find the following logarithm using a calculator. (Round to four decimal places as needed)

$\log\left(5.82\ \times10^7\right)$

(a)

58.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed)

ln(42.11)

(a)

59.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed.

ln(0.0641)

(a)

60.

Use a calculator to find the natural logarithm, base e. (Round to four decimal places as needed)

ln(993.8)

(a)

61.

Find the logarithm. (Round to four decimal places as needed)

$\ln\left(5.17\times e^7\right)$

(a)

62.

Use a calculator to find approximations of the common logarithms. (Round to four decimal places as needed)

log(25.46)

(a)

63.

The hydrogen ion concentration [H+], in a certain cleaning compound is $H^+=2.7\ \times10^{-11}$ . Use the formula $pH\ =\ -\log\left[H^+\right]$ to find the pH of the cleaning compound. (Round to the nearest tenth as needed)

(a)

64.

The loudness L, in decibels (dB), is given by the formula $L=\log\ \frac{I}{I_0}$ where $I_0=10^{-12}$ . The intensity, I, of a sound is $4.3\times10^{-6}$ . How loud in decibels is this sound level? (Round to the nearest whole number)

(a)

65.

The cost benefit equation $T\ =\ -0.699\ -\ 190\ln\left(1\ -\ p\right)$ describes the approximate tax T, in dollars per ton, that would result in p% (in decimal form) reduction in carbon dioxide emissions. What tax will reduce the emissions 45%?

(Round to the nearest dollar)

(a)

66.

Use a scientific calculator to solve the following equation for x.

$5^x=20$

Round to three decimal places

(a)

67.

Solve for x.

$4^{2x}=31$

(Round to 4 decimal places if needed)

(a)

68.

Use natural logarithms to solve the equation.

$e^{-0.851x}=4$

(Type an integer or a decimal rounded to the nearest thousandth)

(a)

69.

Use a scientific calculator to solve the following equation for x. Use natural logarithms.

$\ln e^{0.51x}=\sqrt[]{7}$

(Type an integer or a decimal rounded to three decimal places as needed)

(a)

70.

Solve.

$\log_{10}\left(2x\ -\ 5\right)\ =\ 4$

Simplify your answer. Round to the tenth place.

(a)

71.

Solve the following equation for the variable x. Give exact solutions.

$\log\left(5x+2\right)\ =\ \log5$

(type an integer or simplified fraction)

(a)

72.

Solve for x. $\log\left(7x\right)\ -\ \log\left(x\ -\ 3\right)=\ \log\ 2$

a)

1.2

b)

-1.2

c)

0

d)

No solution

73.

Solve for x. $\log\left(5x\right)\ -\ \log\left(2x\ -\ 3\right)\ =\ \log\ 8$ Simplify your answer as a fraction.

(a)

74.

How much money will there be in an account at the end of 10 years if $17000 is deposited at 3% interest compounded quarterly? (Assume no withdrawals are made.)

(a)

75.

How much money will there be in an account at the end of 8 years if $5000 is deposited at 5.5% annual rate that is compounded continuously? (Assume no withdrawals are made.)

(a)

76.

What is the exact solution to the equation $\ln\left(x-10\right)-\ln\left(5\right)=3$ ?

a)

$x=5e^3+10$

b)

$x=\frac{5e^3}{10}$

c)

$x=e^3+5$

d)

$x=25$

2.8 - 2.14 Review

Total questions: 76

Worksheet time: 4hrs 48mins

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