College Algebra / Unit 8 Alg 457 short lesson, about 20 seconds
The Change-of-Base Formula
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The idea
The change-of-base formula computes any logarithm from a borrowed base: log_b(M) = log(M)/log(b), with the same base upstairs and down.
In practice
log₂(32) = log(32)/log(2) ≈ 1.505/0.301 = 5 — the calculator's two buttons reaching any base.
Where people slip
A quotient of logs is change of base, never the log of a quotient.
Your place on the trail
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