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

If log(100) = 2 and log(10) = 1, what is log(1000)?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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If 2x = 16, what is the value of x?

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What is the sum of the first 50 positive integers?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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What is the LCM of 15 and 20?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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How many diagonals does a pentagon have?

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