College Algebra / Alg 446 · Atom · ~20 seconds
The Product Rule for Logarithms
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The product rule for logarithms turns a product's log into a sum of logs: log_b(MN) = log_b(M) + log_b(N).
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log₂(4 · 8) = log₂(32) = 5, and log₂(4) + log₂(8) = 2 + 3 = 5 — products in, sums out.
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The rule mirrors the product rule of exponents: multiplication adds exponents.
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