Free Printable HA2 Log Review

1.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2

d)

1

2.

When would we use this formula? A = Pe ^rt

a)

interest increases by fixed amount

b)

compound interest

c)

compound continuously

d)

decreases by fixed percent

3.

Evaluate the following logarithm by converting to exponential form.
log_⅕125 = x

a)

x = 3

b)

x = -3

c)

x = 25

d)

x = 5

4.

Expand.

a)

1/3 log x + log y + log z

b)

1/3 log x + 1/3 log y + 1/3 log z

c)

1/3 log x - 1/3 log y - 1/3 log z

d)

3 log x + 3 log y + 3 log z

5.

Simplify the following logarithmic function:
log₂2⁸=

a)

8

b)

2

c)

1

d)

16

6.

Simplify the following:
6^log₆36

a)

6

b)

36

c)

1

d)

2

7.

Write the following equation in logarithmic form:
e³≈ 20.09

a)

ln3 ≈ 20.09

b)

ln20.09 ≈ 3

c)

lne ≈ 3

d)

ln20.09 ≈ e

8.

Expand

a)

4ln3y - 3lnx

b)

ln3 + 4lny - 3lnx

c)

4ln3lny - 3lnx

d)

ln3 + lny⁴ - lnx³

9.

Expand

a)

log₃9 - log₃x + log₃y

b)

log₃9 + log₃x + log₃y

c)

2 - log₃x + log₃y

d)

2 - log₃x - log₃y

10.

Write the inverse:

a)

A

b)

B

c)

C

d)

D

11.

Write the inverse:

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Solve

a)

-3

b)

3

c)

1/3

d)

No solution

14.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

15.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

16.

Solve this log:
log_4.5 3.3

a)

1.260

b)

.794

c)

0.733

d)

0.519

17.

log₂(x + 2) + log₂x = 3

a)

-4, 2

b)

-2, 4

c)

2 ; -4 is extraneous

d)

1 ; -3 is extraneous

18.

Solve: 2^3x = 15

a)

2.3

b)

-2.3

c)

1.3

d)

-1.3

19.

Evaluate log 0.001

a)

-2

b)

-3

c)

1/3

d)

10

20.

ln(e^W)

a)

e

b)

W

c)

e^W

d)

undefined

21.

Match the graph with its equation

a)

y = log₆(-x) + 1

b)

y = log₆(x − 2) + 1

c)

y = log₆(x + 2) - 1

d)

y = log(x-8) + 1

22.

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)

23.

What is the domain?

a)

(-∞, ∞)

b)

(0, ∞)

c)

[1, ∞)

d)

(1, ∞)

24.

Where is the asymptote?

a)

x = 1

b)

y = 1

c)

x = -1

d)

y = -1

25.

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

a)

0

b)

∞

c)

-∞

d)

1

26.

As x --> ∞, f(x) --> ____

a)

0

b)

∞

c)

-∞

d)

1

27.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

28.

The natural logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

29.

log₈(-64)

a)

-8

b)

2

c)

-2

d)

Undefined

30.

Using the change of base property, rewrite log₂31

a)

log(2) / log(31)

b)

log(2/31)

c)

log(31)/log(2)

d)

log(31/2)

31.

Logarithms have a

a)

Vertical Asymptote

b)

Horizontal Asymptote

c)

Linear Asymptote

d)

Diagonal Asymptote

32.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

33.

You invest $5,000 into a savings account that has an interest rate of 5% compounded continuously. In how many years will there be $12000 in the account? ( $y=Pe^{rt}$ )

a)

12.375 Years

b)

177.073 Years

c)

0.175 Years

d)

17.509 Years

34.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

35.

Solve the equation for x.

a)

998

b)

-1.523

c)

0.477

d)

0

36.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

37.

Solve for x:
log₃3^x = 5

a)

5

b)

4

c)

3

d)

243

38.

2 * 4^{3x – 6}– 8 = 120

a)

x = 3

b)

x = 4

c)

x = 2.9

d)

x = 8

39.

Solve: $\log_2\left(x\right)=6^{\log_63}$

a)

$8$

b)

$6$

c)

$9$

d)

None of the above

40.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

41.

Use the change of base rule to rewrite this problem:

log₅75

a)

log(75)/log(5)

b)

log(5)/log(75)

42.

Find the inverse function:
f(x) = 10^x

a)

f^-1(x) = log(x)

b)

f^-1(x) = ln(x)

c)

f^-1(x) = 10^x

d)

f^-1(x) = x¹⁰

43.

Solve for x

2\ln x=0.4

a)

1.221

b)

0.746

c)

1.492

d)

2.226

44.

$6\ +\ \log_2\ x\ =\ 6$

a)

9

b)

$\frac{1}{10}$

c)

1

d)

121

45.

find the asymptote: y = log₁₀ (x+3)

a)

x=-3

b)

x=3

c)

y=-3

d)

y=3

46.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

47.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

48.

$Find\ the\ inverse\ of\ :\ y=\log_9x+4$
HINT: isolate the logarithm first.

a)

$y=9^x+4$

b)

$y=9^x-4$

c)

$y=9^{\left(x-4\right)}$

d)

$y=9^{\left(x+4\right)}$

49.

Simplify the expression: $6^{\log_63x}$

a)

$3x$

b)

$-3x$

c)

$6x$

d)

$-6x$

50.

Simplify

a)

e/15

b)

e

c)

15

d)

1

HA2 Log Review

Total questions: 50

Worksheet time: 3hrs 54mins

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