Topic Details (Notes format)

How to Interpret Logarithmic Scales (pH, Richter, Decibel)

Subject: Mathematics

Book: Maths Mastery

Logarithmic scales measure phenomena spanning huge ranges. pH = –log₁₀[H⁺] gauges acidity, each integer step is a tenfold difference in H⁺ concentration. The Richter scale for earthquakes is log-based, so an increase of 1 indicates 10× greater amplitude. Decibels measure sound intensity, with each 10 dB jump implying a 10× power increase. Understanding logs clarifies why linear changes in these scales represent vast multiplicative shifts. Proficiency ensures correct interpretation of scientific and everyday data, from hearing protection advice to reading environment metrics accurately.

Practice Questions

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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