Exponential equations and inequalities: methods
Take out a common power, substitute t = 2ˣ, read a root off a graph, and decide when an inequality keeps its sign.
- Palestine: grade 11
- Ukraine: grade 11
- Russia: grade 11
Guide
This follows Ukrainian Grade 11 algebra §2–3: besides the same-base method, a common factor, the substitution t = 2x and the graph.
The line is the right side and the curve the left. A root is where they cross; an inequality asks where the curve is above or below the line.
Common slips: losing a term, answering t instead of x, and keeping the sign for a base between 0 and 1.