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.
Time left: 00:00:00
Sample questions
- Calculate log___(___).
- Calculate log___(___) + log___(___).
- Calculate log___(___) − log___(___).
- Calculate ___ · log___(___).
- Calculate 10log10(___).
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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