StudyBrixFree worksheets, study guides and courses

Mathematics · Grades 10–12

Logarithms of products

For real logarithms: b > 0, b ≠ 1, u > 0 and v > 0.

Make a worksheet

The key idea

For real logarithms: b > 0, b ≠ 1, u > 0 and v > 0.

log_b(uv) = log_b(u) + log_b(v)

Worked examples

Evaluate log base 4 of (1024 × 64).

log_4(1024) + log_4(64) = 5 + 3 = 8

8

Evaluate log base 8 of (512 × 512).

log_8(512) + log_8(512) = 3 + 3 = 6

6

Try it yourself

  1. Evaluate log base 3 of (81 × 27).

  2. Evaluate log base 6 of (6 × 6).

Check your understanding

Answers and marking notes
  1. 7

    log_3(81) + log_3(27) = 4 + 3 = 7

  2. 2

    log_6(6) + log_6(6) = 1 + 1 = 2

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

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