Part of ALG-11 — Logarithms, Exponentials & Functional Equations

Key Identity — log_a(b) * log_b(a) = 1

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This follows directly from change of base: logalog_a(b) = 1/logblog_b(a). Useful in simplifying products of logs with swapped bases. Extended: logalog_a(b)logblog_b(c)logclog_c(d) = logalog_a(d) (chain multiplication). Example: log2log_2(3)log3log_3(4)log4log_4(5)*log5log_5(2) = log2log_2(2) = 1.

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