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Grade 11 · Math

Read a logarithm as an exponent

Connect a logarithm with the corresponding exponential statement.

6 authored questions + worked example

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Worked example

Find log base 2 of 8.

Answer & why

Answer: 3

A logarithm gives an exponent: 23 = 8, so log base 2 of 8 is 3.

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All questions

All 6 authored questions for this skill.

Question 1

Find log base 4 of 16.

  1. 3
  2. 1
  3. 4
  4. 2
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 2

A logarithm gives an exponent: 42 = 16, so log base 4 of 16 is 2.

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Question 2

Find log base 5 of 125.

  1. 3
  2. 2
  3. 4
  4. 5
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 3

A logarithm gives an exponent: 53 = 125, so log base 5 of 125 is 3.

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Question 3

Find log base 10 of 10000.

  1. 6
  2. 4
  3. 3
  4. 5
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 4

A logarithm gives an exponent: 104 = 10000, so log base 10 of 10000 is 4.

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Question 4

Find log base 2 of 64.

  1. 7
  2. 6
  3. 5
  4. 8
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 6

A logarithm gives an exponent: 26 = 64, so log base 2 of 64 is 6.

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Question 5

Find log base 2 of 8.

  1. 4
  2. 3
  3. 2
  4. 5
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 3

A logarithm gives an exponent: 23 = 8, so log base 2 of 8 is 3.

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Question 6

Find log base 3 of 27.

  1. 5
  2. 2
  3. 4
  4. 3
A hint

Ask: to what exponent must the base be raised to get the positive argument?

Answer & why

Answer: 3

A logarithm gives an exponent: 33 = 27, so log base 3 of 27 is 3.

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