Laws of Logarithms

The three main laws (same base)

1. Multiplication: log_a(xy) = log_ax + log_ay

2. Division: log_a(x/y) = log_ax - log_ay

3. Power: log_a(xⁿ) = n log_ax

Examples

log 2 + log 5 = log(2×5) = log 10 = 1 (base 10)

log₃27 - log₃9 = log₃(27/9) = log₃3 = 1

log₂8³ = 3 log₂8 = 3×3 = 9

Tip: These are just the index laws written in reverse.

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