Logarithmic & Exponential Form

Name :

Score :

Logarithmic & Exponential Form

Express each equation in logarithmic form.

1) 2 = r

2) a = 128

3) u = 3 5) 4 = 64 7) x = 2

4) 7 = s

6)

3?

?

=

1 9

8) 6 = r

Express each equation in exponential form.

9) log 512 = h

10) log? 36 = 2

11)

log

1 16

= ?y

13) log? 81 = 4

12)

log

p =

1 6

14) log 7 = f

15) log n = 2

16)

log

k =

1 2

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Name :

Answer key

Score :

Express each equation in logarithmic form.

1) 2 = r

2) a = 128

log r = 3 3) u = 3

log 128 = 7 4) 7 = s

log ?

3 =

1 4

5) 4? = 64

log 64 = z 7) x = 2

log s = 6

6)

3?

?

=

1 9

log ?

1 9

=

d

8) 6 = r

log ?

2

=

1 6

log r = 3

Express each equation in exponential form.

9) log 512 = h

10) log? 36 = 2

?

8 = 512

11)

log

1 16

= ?y

4?

=

1 16

13) log 81 = 4

a = 36

12)

log

p =

1 6

64 = p 14) log 7 = f

x = 81 15) log n = 2

49 = 7

16)

log

k =

1 2

11 = n

8 =k

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Name :

Score :

Single Logarithm and Expansion

Expand each expression :

1) log x y m n

=

2) log 5a

=

3) 5 log a b n

=

4)

log ?

b c

=

5) 4 log p q r s

=

Rewrite each expression in single logarithm:

6) (4 log x + 5 log? ? ? ? log? z

=

7) (3 log m + 12 log n? ? 3 log p

=

8)

1 3

(4

log ?

s + log ?

t?

=

9) 40 log t ? (8 log

?

?

?

?

?

?

=

10) 6 (log 5 ? log m?

=

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Name :

Expand each expression :

1) log x y m n

=

2) log 5a

=

3) 5 log a b n

=

4)

log ?

b c

=

5) 4 log p q r s

=

Answer key

Score :

(2 log x + 3 log y? ? (log log n? ?

1 2

(log

5 + 7 log

a?

(10 log a + 5 log b) ? 15 log n

4 (log b ? log c?

(24 log p + 12 log q? ? (8 log r + 4 log s?

Rewrite each expression in single logarithm:

6) (4 log x + 5 log? ? ? ? log? z

=

7) (3 log m + 12 log n? ? 3 log p

=

8)

1 3

(4

log ?

s + log ?

t?

=

9) 40 log t ? (8 log

?

?

?

?

?

?

=

10) 6 (log 5 ? log m?

=

log

x y z

3 log

m n p

log s t

8 log t w x

log

5 m

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Name :

Logarithm - Solve

Score :

Solve for x.

Example 1:

log 4 = x

64 = 4

4? = 4

x =

1 3

Solve for x.

1) log 2 = x

Example 2: log x = 2 5 = ?

?

5? = x x = 625

2) log? 64 = 2

x =

3) log

1 6

= x

x =

5) log

1 8

= x

x =

7)

log?

6 =

1 2

x = 9) log x = 3

x =

4) log

1 16

= x

x =

6)

log?

3 =

1 4

x = 8) log x = 2

x = 10) log 25 = x

x =

x =

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Name :

Score :

Logarithmic Equation

Solve for x.

Example 1:

log 4 = x

64 = 4

4? = 4

x =

1 3

Solve for x.

1) log 2 = x

Example 2: log x = 2 5 = ?

?

5? = x x = 625

2) log? 64 = 2

x =

1 2

3) log

1 6

= x

x =

?1

5) log

1 8

= x

x =

3

7)

log?

6 =

1 2

x = 36 9) log x = 3

x =

2

4) log

1 16

= x

x =

?4

6)

log?

3 =

1 4

x =

81

8) log x = 2

x = 729 10) log 25 = x

x = 64

x =

2 3

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Name :

Logarithm - Solve

Score :

Solve for x.

Example 1: log

?

?

?

?

1 3

= x?5

?

?

?

?

=

1 3

?

?

?

?

= ?

?

?

x = 4

Solve for x.

1) log 6 = x+3

Example 2: log (2x) = 2 8? = (2x) (8? ) = 2x 4 = 2x x = 2

2) log 64 = 2

x =

3) log

1 4

= x?1

x =

5) log

x 8

=

1 5

x =

7)

log

16 = 4

x =

4) log

1 9

= 2x

x = 6) log 625 = 2x+3

x = 8) log (4x) = 2

x = 9) log (x?1) = 3

x = 10) log 2 = 2

x =

x =

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Name :

Answer key

Score :

Solve for x.

Example 1: log

?

?

?

?

1 3

= x?5

?

?

?

?

=

1 3

?

?

?

?

= ?

?

?

x = 4

Solve for x.

1) log 6 = x+3

Example 2: log (2x) = 2 8? = (2x) (8? ) = 2x 4 = 2x x = 2

2) log 64 = 2

x =

?

5 2

3) log

1 4

= x?1

x =

3 5

5) log

x 8

=

1 5

x =

7)

log

16 = 4

x =

8 3

4) log

1 9

= 2x

x =

?1

6) log 625 = 2x+3

x =

?

1 2

8) log (4x) = 2

x =

1

9) log (x?1) = 3

x = 324 10) log 2 = 2

x = 730

x =

1 8

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