Reading & Plotting Logarithmic Graph Paper (Semi-Log & Log-Log)
Logarithmic scale paper is one of the most powerful diagnostic tools in science and engineering. It compresses huge numerical ranges into manageable visual spaces and transforms exponential curves into straight lines.
Understanding Decade Cycles
On a logarithmic axis, the distance between numbers corresponds to the logarithm of the ratio between those numbers. The distance from 1 to 2 is equal to the distance from 10 to 20, or 100 to 200 (\(\log_10(2) \approx 0.301\)).
Each complete sequence from 1 to 10 (or 10 to 100) is called a decade cycle. A 3-decade semi-log sheet allows you to plot data spanning three orders of magnitude (for example: from 10 Hz to 10,000 Hz).
Semi-Log vs Log-Log Decision Tree
Use Semi-Log Paper When:
Your equation follows exponential form \(y = a \cdot e^(bx)\) or \(y = a \cdot 10^(bx)\) (e.g. radioactive decay, population growth, capacitor charging voltage).
Use Log-Log Paper When:
Your equation follows power-law form \(y = a \cdot x^b\) (e.g. Kepler's third law of planetary motion, fluid flow orifice discharge).