Find domain restrictions when applying logarithm laws
Problem
What domain restrictions must be considered when applying log laws to \(\ln(x)+\ln(x-3)\)?
Big Picture
What this problem is really about
Each logarithm contributes its own strict positivity condition. Solve those inequalities separately and intersect them, since every log must exist at the same input. This original common domain remains part of the expression even if a later product-law rewrite appears to have a simpler single argument.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
