Condense a sum or difference of logarithms into one logarithm
Problem
Condense \(\log_b(x)~+~\log_b(5)\) into a \(\text{single}~\text{logarithm}\).
Big Picture
What this problem is really about
Condensing reverses the logarithm laws: a sum of same-base logarithms becomes the logarithm of a product, while a difference would become a quotient. Check every original log argument first and retain their common domain. The operation between the logs determines how the arguments combine; it does not move unchanged inside.
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.
