OCR•A-Level•Mathematics
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Exponentials and Logarithms
Exponential and logarithmic functions, laws of logarithms, and modelling
Practice 20 subtopics in Exponentials and Logarithms. All questions match the OCR A-Level specification.
About Exponentials and Logarithms
Exponentials and Logarithms is a key topic in the OCR A-Level Mathematicsspecification. This topic covers exponential and logarithmic functions, laws of logarithms, and modelling.
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Exponential functions y = aˣGraphs of exponential functionsThe natural exponential e ≈ 2.718The function y = eˣ and its propertiesGraphs of y = eᵏˣDefinition: logₐx = y ⟺ aʸ = xNatural logarithm ln x = logₑxGraphs of logarithmic functionsRelationship between eˣ and ln xlog(xy) = log x + log ylog(x/y) = log x - log ylog(xⁿ) = n log xChange of base formulaSolving equations using logarithmsSolving equations of form aˣ = bEquations reducible to quadratics in eˣExponential growth and decay modelsUsing logarithms to linearise dataDetermining constants from experimental dataComparing exponential models
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