Logarithmic identity, change of base, the logarithmic function
Use the basic logarithmic identity, change base, and compare logarithms with a base between 0 and 1. Section: Grade 11, logarithm properties and the logarithmic function; logarithmic equations are in another studio.
- Ukraine: grade 11
- Russia: grade 11
Guide
This follows Ukrainian Grade 11 algebra §4–5. A logarithm is read off the graph of a^x: log₂32 = 5 because 25 = 32.
The marked points help; the common slips are adding instead of multiplying powers, forgetting that a base can be a power, and assuming a logarithmic function always rises.