Logarithmic equations and inequalities
Solve equations with a sum of logarithms, check roots against the domain, substitute t = lg x, find a variable base, and solve inequalities with a base between 0 and 1.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- Ukraine: grade 11
- Russia: grade 11
Guide
This follows Ukrainian Grade 11 algebra §6–7. Always write the domain first: the argument is positive, the base is positive and not 1. A root outside it is extraneous.
Common slips: keeping an extraneous root, answering t instead of x, a negative base, and keeping the sign for a base below 1 or forgetting the domain.