Expanding log₃(x²y/z³)

Algebra 2 · Axiom Academy

Apply the quotient, product, and power rules to expand into separate terms. Expand into a sum and difference of individual logarithms, using the quotient, product, and power rules. Nice work — you fully expanded a logarithm of a quotient, product, and power. The pieces worth keeping: Quotient Rule: — splits a division inside a log into a difference. Product Rule: — splits a multiplication inside a log into a sum. Power Rule: — brings an exponent out front as a coefficient. Order matters: work from the outside in — division, then multiplication, then exponents. Every expanded term keeps the same base, . These three properties work for logarithms of any base — you'll use them constantly to simplify and solve logarithmic equations throughout Algebra 2.

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