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The Product Rule for Logarithms

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State

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.

Watch for

The rule mirrors the product rule of exponents: multiplication adds exponents.

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