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1.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

2.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

3.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

4.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

5.

Rewrite the equation into logarithmic form:
6² = 36

a)

log₆ 2 = 36

b)

log₆ 36 = 2

c)

ln 36 = 2

d)

6³⁶ = 2

6.

Evaluate log₈ 8 by thinking 8 to what power is 8, so the answer is

a)

8

b)

-1

c)

0

d)

1

7.

Condense

a)

A

b)

B

c)

C

d)

D

8.

Condense

a)

A

b)

B

c)

C

d)

D

9.

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

10.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

11.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

12.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

13.

Write as a single log: log 12 + 2 log x

a)

log (12 + 2x)

b)

log (14x)

c)

log (12 * 2x)

d)

log (12x²)

14.

a)

log(x) + log(z) + 4log(y)

b)

3log(x) − log(z) − 4log(y)

c)

3log(x) + log(z) + 4log(y)

d)

log(x) − 4log(z) − 3log(y)

15.

a)

60 log(ab)

b)

6log(a) + log(b)

c)

log(a) - 30 log(b)

d)

6log(a) + 30 log(b)

16.

Expand

a)

A

b)

B

c)

C

d)

D

17.

Solve

a)

b)

c)

d)

18.

Solve

a)

b)

c)

19.

Solve

a)

b)

c)

20.

Solve

a)

b)

c)

21.

Condense

a)

log₈(a¹⁸/b³)

b)

log₈(a¹⁸b³)

c)

log₈(a/b³)

d)

15log₈(a/b³)

22.

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

23.

Rewrite log_b(xⁿ)

a)

nlog_bx

b)

(log_bx)ⁿ

c)

xⁿlog_bx

d)

log_b(xⁿ)

24.

Write the expression as a single logarithm. Then simplify if possible.
log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

25.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

26.

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

27.

Simplify log₄4^3x

a)

3x

b)

3

c)

4

d)

4^3x

28.

Expand: $\log_6\left(\frac{5}{4y}\right)$

a)

$\log_65\ +\ \log_64\ +\ \log_6y$

b)

$\log_65\ -\ \log_64\ +\ \log_6y$

c)

$\log_65\ -\ \log_64\ -\ \log_6y$

d)

$\log_65\ -\ \log_64y$

29.

Expand: $\log_4\left(3x^2\right)$

a)

$2\log_43x$

b)

$2\log_43\ +\ 2\log_4x$

c)

$\log_43\ +\ 2\log_4x$

d)

$2\log_43\ +\ \log_4x$

30.

Condense: $\frac{1}{2}\log_3x\ +\ 5\log_3y$

a)

$\log_3\left(\sqrt{x}y^5\right)$

b)

$\log_3\left(\sqrt{x}y^5\right)$

c)

$\log_3\left(5\sqrt{x}y\right)$

d)

$\log_3\left(xy\right)^{\frac{5}{2}}$

31.

Condense the Logarithm $5\log_{ }a\ -\ 25\log_{ }b$

a)

$\log\ \left(a^5+b^{25}\right)$

b)

$\log\ \left(a^5-b^{25}\right)$

c)

$\log\ \left(ab\right)^{25}$

d)

$\log_{ }\ \left(\frac{a^5}{b^{25}}\right)$

32.

Simplify: $\log_4\left(x+4\right)-\log_4\left(x-5\right)$

a)

$\log_49$

b)

$\log_4\left(2x-1\right)$

c)

$\log_4\left(x^2-x-20\right)$

d)

$\log_4\left(\frac{x+4}{x-5}\right)$

33.

Simplify: $2\log_3\left(11x\right)$

a)

$\log_3\left(22x\right)$

b)

$\log_3\left(121x\right)$

c)

$\log_3\left(121x^2\right)$

d)

$\log_3\left(11x^2\right)$

34.

Expand the logarithm.
$\log\frac{x}{y^6}$

a)

$\log x+6\log y$

b)

$\log x-6\log y$

c)

$\log x+\log6y$

d)

$\log x-\log6y$

35.

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

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Total questions: 35

Worksheet time: 4hrs 36mins

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