Pure · Exponentials & logarithms
Chapter 1 · 3
The idea
The laws of logarithms
The product, quotient and power laws — turning sums and differences of logs into a single log (and back) — plus log_a a = 1, log_a 1 = 0 and the reciprocal rule.
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Pure · Exponentials & logarithms
The laws of logarithms
The product, quotient and power laws — turning sums and differences of logs into a single log (and back) — plus log_a a = 1, log_a 1 = 0 and the reciprocal rule.
Why it works
Logs turn hard operations into easy ones
A logarithm answers "what power?" — and powers have their own arithmetic. When you multiply powers of the same base, the exponents add: . Since logs ARE exponents, that one fact flips into the headline law of this page: the log of a product is a sum of logs. Multiplication becomes addition, division becomes subtraction, powers become multiples — every law here is an index law seen through the inverse.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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