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

The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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What is the sum of all even numbers between 1 and 50?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the value of log₃(27)?

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If x - y = 5 and x + y = 15, what is the value of x?

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What is the LCM of 15 and 20?

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