Condensing log(x) + 2log(y) - 3log(z)

Algebra 2 · Axiom Academy

Combine three logarithmic terms into one using the Power, Sum, and Difference Rules. Condense into a single logarithm using the properties of logarithms. Nice work — you condensed a three-term logarithmic expression into a single logarithm. Remember these key properties: Power Rule: A coefficient in front of a log becomes an exponent inside it: . Sum Rule: Addition of logs becomes multiplication inside a single log: . Difference Rule: Subtraction of logs becomes division inside a single log: . Order matters: Apply the Power Rule to every coefficient first, then combine using the Sum and Difference Rules. This reverse process — condensing instead of expanding — is exactly what you need to solve logarithmic equations, where a single logarithm is far easier to work with than three.

This is the written version of the interactive lesson above. See the full Algebra 2 course.