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Test: Logarithms and their properties

This test develops understanding of the definition of a logarithm and its relationship with exponents. Tasks apply product, quotient and power properties, transform expressions and check domain restrictions.

Question qty: 10
Duration in minutes: 13
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Sample questions

  • What restriction applies to a logarithm argument?
  • What does log_a(b) mean?
  • Calculate log_a(v).
  • Calculate log_a(m) + log_a(n).
  • Calculate log_a(m) − log_a(n).
  • Calculate k · log_a(v).
  • Calculate 10^(log₁₀(b)).
  • Calculate log₁₀(v).

Logarithms and their properties

The logarithm logₐb is the exponent to which base a must be raised to obtain b: logₐb = c exactly when aᶜ = b. The conditions are a > 0, a ≠ 1 and b > 0.

Operational rules

The logarithm of a product is a sum, that of a quotient is a difference, and an exponent may be brought in front. Change base using logₐb = log_cb/log_ca. These rules require positive arguments, and the logarithm of a sum cannot be split into logarithms of its terms.

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