Free Printable Logarithmic Functions Graph and Properties

1.

Convert the log form to exponent form and find the value of x. $\log_{10}(x)=2$ .

a)

100

b)

10

c)

1000

d)

0.01

2.

Fill in the blank for the exponent form: $10^2=100$ .

Logarithmic Form: $\log\ \left(\ 100\right)\ =\ -----$

a)

1

b)

2

c)

3

d)

4

3.

Convert logarithm form to exponent form. $\log_a(z)=c$

a)

$z^a=c$

b)

$ac=z$

c)

$a^c=z$

d)

$c^z=a$

4.

Find the domain of the function: f(x) = log_3 (x + 5) - 2.

a)

y < 5

b)

x < -5

c)

x > -5

d)

y > -5

5.

Find the range of the function. $\log_2(x-4)-3$

a)

x > 4

b)

y > -4

c)

y > -3

d)

All real numbers

6.

$f\left(x\right)=\log\left(x-6\right)+7$ for What is the value of x, $f(x)=0$ ?

a)

5

b)

6

c)

7

d)

8

7.

What is the x intercept of the function $f(x)=\log_5(x+1)-3$ ?

a)

(0, -124)

b)

(124, 0)

c)

(126, 0)

d)

(-126, 0)

8.

What is the y intercept of the function $f(x)=\log_5(x+1)-5$ ?

a)

(1, 0)

b)

(0, -1)

c)

(-5, 0)

d)

(0, -5)

9.

Calculate the value of x. Given $\log_3(x)=3$

a)

9

b)

27

c)

81

d)

3

10.

Use properties of the logarithms to match the expressions: log(4x) = log4 + logx

a)

Equality Rule

b)

Product Rule

c)

Quotient Rule

d)

Power Rule

11.

Use properties of the logarithms to match the expressions: $\log\left(\frac{7}{y}\right)=\log7-\log y$

a)

Equality Rule

b)

Product Rule

c)

Quotient Rule

d)

Power Rule

12.

Use properties of the logarithms to match the expressions: $\log(y^2)=2\log y$

a)

Equality Rule

b)

Product Rule

c)

Quotient Rule

d)

Power Rule

13.

Use properties of the logarithms to match the expressions: If log(x) = log(y), then x=y

a)

Equality Rule

b)

Product Rule

c)

Quotient Rule

d)

Power Rule

14.

Use the properties of logarithms to find $\log(29\cdot59)$ . Write your answer in nearest hundredth.

(a)

15.

Use the properties of logarithms to find ln(19/4).

4 lines

16.

Use the properties of logarithms to find $\log\left(5\right)^3$

a)

$3\cdot\log(5)$

b)

$\log(5\cdot3)$

c)

3 + log(5)

d)

$\log(5)^3$

17.

Evaluate log₂ 64.

a)

6

b)

5

c)

4

d)

3

18.

Evaluate log_4 4123

a)

124

b)

123

c)

1

d)

4

19.

Evaluate $e^{\ln60}$

a)

1

b)

e

c)

6

d)

60

20.

Describe the transformation of the function log(x - 5) + 2.

a)

up 2 units

b)

right 5 units

c)

down 2 units

d)

reflect over x axis

e)

left 5 units

21.

For the function (2log(x + 6) - 7), select all the transformations that apply:

a)

Stretch vertically by a factor of 2, left 6 units, down 7 units

b)

Stretch horizontally by a factor of 2, right 6 units, up 7 units

c)

Reflect over x axis

d)

Stretch vertically by a factor of 1/2

22.

Solve for x (rounded to hundredth places) for the equation log(x) + log(19) = log(5):

4 lines

23.

Solve for x: $\log(9x)=\log(12x+9)$

a)

x = -1

b)

x = 5

c)

x = 0

d)

x = -3

24.

What is the value of x if log₆ x = 2?

a)

2

b)

6

c)

1/36

d)

36

25.

What is the value of x if ln e = x?

a)

-2

b)

1

c)

2

d)

-1

26.

Write log₂ 0.25 = -2 in exponential form

a)

-2²= 0.25

b)

-2^0.25= 2

c)

2^-2= 0.25

d)

No correct answer

27.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

28.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

29.

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

30.

Rewrite the exponential equation $5^3 = 125$ as a logarithmic equation.

a)

$\log_5 125 = 3$

b)

$\log_3 125 = 5$

c)

$\log_5 3 = 125$

d)

$\log_{125} 5 = 3$

31.

Rewrite the equation in logarithmic form: $64^{\frac{1}{2}}=8$ ?

a)

$\log_{64}\ 8=\frac{1}{2}$

b)

$\log_8\ 64=\frac{1}{2}$

c)

$\log_8\ \frac{1}{2}=64$

d)

$\log_{64}\ \frac{1}{2}=8$

32.

Which of the following is the correct graph for the logarithmic function $f(x) = \log_2(x-3)$ ?

a)

Graph passing through $(4,0)$ with a vertical asymptote at $x = 3$

b)

Graph passing through $(3,0)$ with a vertical asymptote at $x = 0$

c)

Graph passing through $(0,3)$ with a vertical asymptote at $x = -3$

d)

Graph passing through $(0,0)$ with no vertical asymptote

33.

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

34.

Graph the logarithmic function: $y = \log(x-2)$

a)

The graph is a curve that passes through (3,0) and approaches the line $x=2$ asymptotically.

b)

The graph is a straight line passing through the origin.

c)

The graph is a parabola opening upwards.

d)

The graph is a hyperbola.

35.

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

36.

Find the corresponding graph of
$-\log_2\left(x\right)+3$

a)

b)

c)

d)

37.

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

a)

b)

c)

d)

38.

Rewrite the following in the form $\log\left(c\right)$ :

$\log\left(a\right)+\log\left(b\right)+\log\left(c\right)$

(a)

39.

The $\ln\ e=$ (a)

The $\log10^x$ = (b)

The $\ln e^{abc}$ = (c)

The $\log_bb^{YODA}$ = (d)

Choose from the below words

1

x

abc

YODA

DARTH VADER

0

y

123

40.

Evaluate using properties of logarithms (no calculator): $3\ln e\ \ +\ 2\ln1$

(a)

41.

Expand: $\log\ ab$

a)

$\log a\ -\ \log b$

b)

$b\log a$

c)

$a\log b$

d)

$\log a+\log b$

42.

Simplify: $\frac{1}{4}\log_281+\frac{1}{2}\log_249$

a)

$\log_221$

b)

$\log_210$

c)

$\log_2\left(\frac{3}{7}\right)$

d)

$\log_244.75$

43.

Simplify: $\log_73+\log_76$

a)

$\log_79$

b)

$\log_7\left(\frac{1}{2}\right)$

c)

$\log_718$

d)

$\log_7729$

44.

Write log_b(xy) as two logs

a)

log_bx+log_by

b)

log_bx-log_by

c)

log_bx*log_by

d)

log_bx/log_by

45.

Graph

a)

A

b)

B

c)

C

d)

D

46.

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

47.

Find the corresponding graph of
$\log_3\left(x\right)-2$

a)

b)

c)

d)

Logarithmic Functions Graph and Properties

Total questions: 47

Worksheet time: 44mins

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