Free Printable Log and Exponential Form

1.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

2.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

3.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

4.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

5.

Convert 6^(x+2)=216 to logarithmic form

a)

log₂₁₆(x+2)=6

b)

log₆(x+2)=216

c)

log₆(216)=x+2

d)

log_(x+2)(216)=6

6.

Convert log₈(x+2)=3 to exponential form.

a)

8^(x+2)=3

b)

3^(x+2)=8

c)

8³=x+2

d)

3⁸=x+2

7.

Convert 10^(x+5)=100 to logarithmic form.

a)

log₁₀₀=x+5

b)

log(x+5)=100

c)

log(100)=x+5

d)

log_(x+5)(100)=10

8.

Convert log(x)=y+2 to exponential form.

a)

10^(y+2)=x

b)

1^x=y+2

c)

10^x=y+2

d)

x^(y+2)=10

9.

Convert 2^x+6=10 to logarithmic form

a)

log₄(x)=2

b)

log₂(4)=x

c)

log₂(10)=6

d)

log₂(x)=4

10.

Solve for x.
log_x(64)=3

a)

x=8

b)

x=4

c)

x=3

d)

x=64

11.

Convert log₁₂(x)=2 to exponential form.

a)

12²=x

b)

12^x=2

c)

x²=12

d)

2^x=12

12.

Write the inverse function: t $t=m^x$

a)

$\log_tx=m$

b)

$\log_mx=t$

c)

$\log_mt=x$

d)

$\log_tm=x$

13.

Write the inverse function: $24^x=a$

a)

$\log_{24}x=a$

b)

$\log_{24}a=x$

c)

$\log_xa=24$

d)

$\log_ax=24$

14.

Write the inverse function: $7\left(3\right)^x+12=117$

a)

$\log_{21}12=117$

b)

$\log_{21}105=x$

c)

$\log_312=x$

d)

$\log_315=x$

15.

Write the inverse function: $\log_bx=y$

a)

$b^x=y$

b)

$b^y=x$

c)

$x^y=b$

d)

$y^b=x$

16.

Write the inverse function: $5=\log_7a$

a)

$5^7=a$

b)

$7^a=5$

c)

$a=7^5$

d)

$7=5^a$

17.

Write the inverse function: $8\log_y\left(10\right)-15=1$

a)

$2^y=10$

b)

$10^y=2$

c)

$y^2=10$

d)

$10=2^y$

18.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

19.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

20.

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

21.

Match the graph with its equation

a)

y = log₅ (x + 1) + 1

b)

y = log₅ (x - 1) + 1

c)

y = log₅ (x²) + 1

d)

y = log₅ (x)-1

22.

Select all the transformations that apply.

y = -2 log _1/2x

a)

Vertical stretch by 2

b)

Vertical shrink by 1/2

c)

Reflection across the y-axis

d)

Reflection across the x-axis

23.

Find the corresponding graph of
$-\log_4\left(x+1\right)+2$

a)

b)

c)

d)

24.

What is the domain and range of this graph?

a)

D: all real numbers
R: all real numbers

b)

D: all real numbers
R: y ≥ 0

c)

D: x ≥ 2
R: y ≥ 3

d)

D: x ≤ 2
R: y ≤ 3

25.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

26.

Which graph best represents the following logarithmic function?
$y=\log_4x$

a)

b)

c)

d)

27.

Which graph best represents the following logarithmic function?
$y=\log_2x$

a)

b)

c)

d)

28.

Your parents deposited $2000 when you were born in an account that pays 3% interest and is compounded monthly. How much will you have on your 20th birthday?

a)

$41216.64

b)

$3644.24

c)

6257.12

d)

$3641.51

29.

You deposit $5500 in an account that is compounded continuously at 1.5%, how much will you have in 7 years?

a)

$6108.91

b)

$15717.08

c)

$39081.85

d)

$6104.15

30.

How are exponential and log functions related?

a)

They are cousins

b)

They are siblings

c)

They are married

d)

They are inverses

31.

How does the graph of y=log (x-2) shift?

a)

right 2

b)

left 2

c)

up 2

d)

down 2

32.

Where is the asymptote for y=log (x-2)?

a)

y=2

b)

y=-2

c)

x=2

d)

x=-2

33.

What is the equation of the asymptote?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

34.

Which function has a vertical asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

35.

Which function has a horizontal asymptote?

a)

exponential

b)

logarithm

c)

both

d)

neither

36.

What is the transformation?

a)

Vertical Translation up 1

b)

Vertical Translation down 1

c)

Horizontal Translation left 1

d)

Horizontal Translation right 1

37.

What is the HA?

a)

y = 1

b)

y = 0

c)

x = 0

d)

y = -1

38.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

39.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

40.

What is the HA?

a)

y = -2

b)

y= 2

c)

y = 0

d)

y = 1

41.

Is this exponential growth or decay?

a)

Growth

b)

Decay

42.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

43.

What is the Range?

a)

(-infinity, infinity)

b)

(-infinity,0)

c)

(0, infinity)

d)

None

44.

What is the y-intercept of the function $y=4\left(5\right)^x?$

a)

(0, 0)

b)

(0, 4)

c)

(0, 5)

45.

What is the asymptote of the function $y=4\left(5\right)^x?$

a)

y = 0

b)

y = 4

c)

y = 5

46.

For $y=a\left(b\right)^x+k$ , how does adding a constant transform the parent function?

a)

Horizontal shift

b)

Vertical Shift

c)

Reflection over the x-axis

d)

Reflection over the y-axis

47.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

48.

How has the function $-5\left(3\right)^x$ been transformed from the parent function $5\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

49.

How has the function $-5\left(3\right)^x$ been transformed from the parent function $5\left(3\right)^x$ ?

a)

Shifted up 4

b)

Shifted down 4

c)

Shifted down 5

d)

Reflection over the x-axis

e)

Reflection over the y-axis

50.

Identify the y-intercept of the function $-3\left(3\right)^x+4$

a)

y-intercept at (0, -3)

b)

y-intercept at (0, 1)

c)

y-intercept at (0, -7)

51.

Identify the asymptote of the function $-3\left(3\right)^x+4$

a)

y = -3

b)

y = 1

c)

y = 4

52.

a)

$-3\left(3\right)^x+2$

b)

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

c)

$-3\left(3\right)^x-2$

d)

$-3\left(\frac{1}{3}\right)^x-2$

53.

a)

$-3\left(4\right)^x+2$

b)

$-3\left(\frac{1}{4}\right)^x+2$

c)

$3\left(4\right)^x+2$

d)

$3\left(\frac{1}{4}\right)^x+2$

54.

If g(x) is a transformation of f(x), describe the transformation.

$g\left(x\right)=\left(2\right)0.25^x$
$f\left(x\right)=0.25^x$

a)

Horizontal stretch

b)

Horizontal compression

c)

Vertical stretch

d)

Vertical compression

55.

If g(x) is a transformation of f(x), describe the transformation.

$f\left(x\right)=-3^x$
$g\left(x\right)=-3^{0.2x}$

a)

Vertical reflection

b)

Vertical stretch

c)

Horizontal stretch

d)

Horizontal compression

56.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

57.

What is the domain of the function shown below?

a)

-2 < x < 5

b)

0 < x < 12

c)

y > 0

d)

All Real Numbers

58.

What is the range of the function shown below?

a)

0 < y < 12

b)

-2 < y < 5

c)

y > 0

d)

All Real Numbers

59.

Which represents exponential decay?

a)

A

b)

B

c)

C

d)

D

60.

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4+ 5

a)

x=4

b)

y=4

c)

x=5

d)

y=5

61.

Determine the range for the function

f(x) = 3(2)^x-4+ 5

a)

[5,∞)

b)

(5,∞)

c)

[4,∞)

d)

(4,∞)

62.

a)

f(x)=2^x-1-3

b)

f(x)=2^x-1+3

c)

f(x)=2^x+1-3

d)

f(x)=2^x+1+3

63.

Which of the following is an exponential decay? (Check all that apply)

a)

y = 5⋅(1/5)^x

b)

y = 5⋅(7/2)^x

c)

y = 5⋅8^x

d)

y = 5⋅1.5^x

Log and Exponential Form

Total questions: 63

Worksheet time: 2hrs 35mins

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