Free Printable The Log Function

1.

Evaluate:

$\log_6\left(1\right)=x$

a)

x = 1

b)

x = 0

c)

x = 6

d)

x = -1

2.

Write in a log form
$3^5=y$

a)

$\log_3y=15$

b)

$\log_5y=3$

c)

$\log_3y=3$

d)

$\log_3y=5$

3.

What number must fill in the blank to make this equation true?

$\log_3\ x=3$

a)

x = 3

b)

x = 1

c)

x = 9

d)

x = 27

4.

Write in exponential form. log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

5.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

6.

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

7.

Rewrite in exponential form:

log₉x=2

a)

9^x=2

b)

2^x=9

c)

2⁹=x

d)

9²=x

8.

Write 6^x = 8 in log form.

a)

log₆ 8 = x

b)

log₈ 6 = x

c)

log₆ x = 8

d)

log₈ x = 6

9.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

10.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

11.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

12.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

13.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

14.

log (-1) =

a)

0.1

b)

.01

c)

all real numbers

d)

does not exist

15.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

16.

Evaluate log_b(b)

a)

-1

b)

0

c)

1

d)

b

17.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

18.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

19.

Evaluate log₇ 343

a)

3

b)

49

c)

7

d)

1

20.

How are exponential and log functions related?

a)

They are cousins

b)

They are siblings

c)

They are married

d)

They are inverses

21.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

22.

Solve for x.
3^x = 27

a)

2

b)

4

c)

3

d)

5

23.

a)

log (xy³)

b)

log (x⁶− y³)

c)

log (x⁶/y³)

d)

log (x⁶ + y³)

24.

log (2 * 3) = ?

a)

log 2 + log 3

b)

log 2 * log 3

c)

log 2 - log 3

d)

log 5

25.

log (3²) =?

a)

log 6

b)

2 log 3

c)

log₂ 3

d)

log₃ 2

26.

log (a * b) = ?

a)

log a * log b

b)

log a + log b

c)

log a - log b

d)

a*log b

27.

log (a² * b) = ?

a)

2log(a) + log(b)

b)

2log(a) + 2log(b)

c)

log(a) + log(b)

d)

2log(a) * log(b)

28.

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

29.

Condense

$\log_39+\log_33$

a)

$\log_312$

b)

$\log_327$

c)

$\log_39$

30.

Condense

\log_5y-\log_525

a)

$\log_5\left(y-25\right)$

b)

$\log_5\left(25y\right)$

c)

$\log_5\left(\frac{y}{25}\right)$

d)

$\log_5\left(\frac{25}{y}\right)$

31.

Which expression is equivalent to $\log_2\left(\frac{m^4}{n^7}\right)$

a)

$4\log_2m+7\log_2n$

b)

$7\log_2m+4\log_2n$

c)

$4\log_2m-7\log_2n$

d)

$7\log_2m-4\log_2n$

32.

Condense: log₂6+log₂3=

a)

log₂18

b)

log₂2 = 1

c)

log₂3

d)

log₂9

33.

Rewrite in exponential form:
ln(2) = x

a)

2^x= 10

b)

10² = x

c)

e^x= 2

d)

e² = x

34.

Condense: log16 + log2 - log8

a)

log4

b)

log8

c)

log10

d)

log24

35.

When you have two log expressions separated by a minus sign (-), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

36.

When you have two log expressions separated by a plus sign (+), we really need to ___________ them to simplify into one log expression.

a)

add

b)

subtract

c)

multiply

d)

divide

37.

Condense into a single logarithm.
$\log_25+\log_29+\log_2w$

a)

$\log_2\left(14w\right)$

b)

$\log_2\left(45w\right)$

c)

$\log_2\left(\frac{14}{w}\right)$

d)

$\log_2\left(14+w\right)$

38.

Condense the following logarithm

\log_3\left(p-2\right)-\log_3x

a)

$\log_3\left(p-2\right)^x$

b)

$\log_3x\left(p-2\right)$

c)

$p-2=x$

d)

$\log_3\left(\frac{p-2}{x}\right)$

39.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

40.

Condense into a single logarithm.
$4\log_7x-3\log_7y$

a)

$\log_7\left(x^{12}y^3\right)$

b)

$\log_7\left(12xy\right)$

c)

$\log_7\left(\frac{x^4}{y^3}\right)$

d)

$\log_4\left(\frac{4x}{3y}\right)$

41.

$\log_9x+\log_9\left(x+2\right)=\log_9\left(35\right)$

a)

5

b)

5, -7

c)

-7

d)

-7, -13

42.

Rewrite 1.6^(x+2) = 14.1

a)

log_1.614.1 = x+2

b)

log_1.6(x+2) = 14.1

c)

log_14.1(x+2) = 1.6

d)

log_(x+2)1.6 = 14.1

43.

Without a calculator, evaluate log₄1

a)

¹/₄

b)

0

c)

-1

d)

not possible

44.

Without a calculator, evaluate log₁₂₅ 25

a)

²/₃

b)

³/₂

c)

¹/₆

d)

¹/₅

45.

Convert log₁₂(x)=2 to exponential form.

a)

12²=x

b)

12^x=2

c)

x²=12

d)

2^x=12

46.

Solve for x.
log_x(64)=3

a)

x=8

b)

x=4

c)

x=3

d)

x=64

47.

A logarithm is always represents

a)

an exponent.

b)

a base.

c)

an answer.

d)

a unicorn.

48.

$\log_8\left(2\right)=\frac{1}{3}$ In the expression, 8 is the

a)

base.

b)

exponent.

c)

argument.

d)

answer.

49.

Rewrite the equation in exponential form.
$\log_8\left(512\right)=3$

a)

$8^{512}=3$

b)

$3^8=512$

c)

$8^3=512$

d)

$3^{512}=8$

50.

Rewrite the equation in logarithmic form.
$5^{-4}=\frac{1}{625}$

a)

$\log_5\left(-4\right)=\frac{1}{625}$

b)

$\log_5\left(\frac{1}{625}\right)=-4$

c)

$\log_{-4}\left(\frac{1}{625}\right)=5$

d)

$\log_{\frac{1}{625}}\left(5\right)=-4$

The Log Function

Total questions: 50

Worksheet time: 2hrs 52mins

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