Logarithms — multiplication made addition, and the grammar of the senses

The logarithm turns multiplication into addition: log(15) = log(3)+log(5), sealed. That one property made calculation possible before computers (Napier 1614 -> slide rules -> every engineer until 1970), and it is the exact INVERSE of the exponential that is the spine of this whole map: the capacitor's RC clock, radioactive decay, compound interest, the diode's curve all rise by multiplying; the logarithm brings them back by adding. One law, read two directions. And the senses are logarithmic — we register ratios, not differences (Weber-Fechner). All sealed (https://narrowhighway.com/s/a8e09bb2b249b5f342d57946144fc09009519a25bc9bbf4b5f76cace64e522f5): sound in decibels (+3 dB = x2 power, 10*log10(2)=3.01); earthquakes on the Richter scale (each step x10 shaking, x31.6 ENERGY = 10^1.5 — the null "x2" caught: https://narrowhighway.com/s/50bb768f74437a29217f63c1820576dec6858f6471b91300ccc9f4ddb7400fc2); music by octaves ((2^(1/12))^12 = 2 exactly, a semitone = 1.0594); stars by magnitude ((100^(1/5))^5 = 100, five magnitudes = x100 brightness, Hipparchus 130 BC); acidity by pH (-log10(10^-4) = 4). A whisper and a jet both fit in one mind because the ear compresses by ratio. The hidden rhyme: the +3 dB doubling and Benford's Law (a real-world number leads with '1' 30.1% of the time) are the SAME constant, log10(2) = 0.301 — both sealed to 301. And the logarithmic spiral (same equation) draws the nautilus, the hurricane, and the arms of galaxies, tying to the golden ratio in the numbers wing. Grade: every identity and scale-constant SEALED; Weber-Fechner is a MEASURED law of perception (why the nervous system compresses logarithmically is real neuroscience, empirical, not derived). Signpost, held lightly: ears and eyes built to hear in proportion. The inverse of the exponential every clock in the map runs on, and the grammar of the senses that read all of it.