A-level · Exponentials & logarithms

Logarithms and non-linear dataExam-style questions

Turning curved laws into straight lines with logs — y = ax^n becomes log-log linear, y = ab^x becomes log-linear — then reading the constants off the gradient and intercept.

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17 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Figure 1(−4.5, 0)(0, 3)Olog₁₀ xlog₁₀ yFigure 1 shows a linear relationship between log⁡10y\log_{10} y and log⁡10x\log_{10} x

    The line passes through the points (−4.5,0)(-4.5, 0) and (0,3)(0, 3) as shown.
    (a) Find an equation linking log⁡10y\log_{10} y with log⁡10x\log_{10} x

    (2 marks)
    (b) Hence, or otherwise, express yy in the form pxqpx^q where pp and qq are rational constants.

    (3 marks)
    Level 2 · 5 marksTry it