College Algebra / Unit 8 Alg 446 short lesson, about 20 seconds
The Product Rule for Logarithms
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The idea
The product rule for logarithms turns a product's log into a sum of logs: log_b(MN) = log_b(M) + log_b(N).
In practice
log₂(4 · 8) = log₂(32) = 5, and log₂(4) + log₂(8) = 2 + 3 = 5 — products in, sums out.
Where people slip
The rule mirrors the product rule of exponents: multiplication adds exponents.
Your place on the trail
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Builds on
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Unlocks
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