Logarithms & powers

Powers

100

How much is 2³?

8

200

How much is 3⁴?

81

300

How much is 8^-2?

1/64

400

How much is 9^3/2?

27

500

How much is 0.5^-10?

1024

Operations on powers

100

Which number is larger? (2²)³ or 2³*2²?

(2²)³

200

Which of these numbers is larger: (0.3³)^-2 or (0.3)³*(0.3)^-2?

(0.3³)^-2

300

Calculate: 18⁴/9⁴

16

400

Calculate: 25³*0.5^-6

1 000 000

500

This expression can be written in the form 2^a. Find the value of a.

0.25*2⁷ⁿ⁺⁵:(2²)ⁿ

a=5n+3

Logs

100

How much is log100?

2

200

How much is log₂(64)?

6

300

How much is log₄32?

5/2

400

How much is log(0.000001)?

-6

500

How much is log₂₇(81)?

4/3

Logs 2

100

log₃a=27. Find the value of a.

a=3

200

log₄a=-2. Find the value of a.

a=1/16

300

Calculate log₈4

2/3

400

log_a125=3. Find the value of a.

a=5

500

log_a512=4.5. Find the value of a.

a=4

Operations on logarithms

100

Calculate: log₂7-log₂56

-3

200

Calculate: log₂6+log₂12-log₂(9/4)

5

300

log(a)=2. Calculate: log(a^-7)

-14

400

Write as a single logarithm: log₂3-4

log₂(3/16)

500

log_ab=x, log_ac=y. Write down in terms of x and y:

 log_a(c⁷/b⁵)

7y-5x