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Mathematics · Grades 10–12

Logarithms as exponents

A logarithm asks which exponent produces the argument.

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The key idea

A logarithm asks which exponent produces the argument.

log_b(a) = x ↔ bˣ = a; a > 0, b > 0, b ≠ 1

Worked examples

Find log base 6 of 216.

6^3 = 216

3

Find log base 3 of 9.

3^2 = 9

2

Try it yourself

  1. Find log base 10 of 100000.

  2. Find log base 4 of 1024.

Check your understanding

Answers and marking notes
  1. 5

    10^5 = 100000

  2. 5

    4^5 = 1024

Further reading and review references

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Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.