The Math Meridian
Back to Exponential and Logarithmic Functions

Semi-log plots and linearizing exponential data

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Useful for: AP® Precalculus IB Math AI SL & HL

Learn it If y = a·bˣ, then log y = log a + x log b: plotting log y against x gives a straight line with slope log b and intercept log a. A straight semi-log plot means the data are exponential.

Example: On a semi-log plot, log y = 0.3x + 1. Find y = a·bˣ.

  1. log a = 1 → a = 10.
  2. log b = 0.3 → b = 10^0.3 ≈ 2.0.
  3. y ≈ 10(2.0)ˣ.

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