Learning objective
F3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x.
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Topic
Pure Mathematics
Subtopic
Logarithmic functions
Aqa A Level MathematicsPaper 1
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Quick explanation
F3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x
- This point belongs to Pure Mathematics, especially Logarithmic functions.
- You need to be able to f3 Know and use the definition of log_a x as the inverse of a^x, where a is positive and x >= 0; know and use the function ln x and its graph; know and use ln x as the inverse function of e^x.
- The key ideas to know are inverse, definition, and positive.
- Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.
Key concepts
inversedefinitionpositivewhereknow
Why it matters
This objective helps connect Logarithmic functions to exam-style questions, flashcards, and revision notes for Pure Mathematics.
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Open revision notesRelated learning objectives
- A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs.
Proof
- B1 Understand and use the laws of indices for all rational exponents.
Laws of indices
- B2 Use and manipulate surds, including rationalising the denominator.
Surds
- B3 Work with quadratic functions and their graphs; use the discriminant including the conditions for real and repeated roots; complete the square; solve quadratic equations including solving quadratic equations in a function of the unknown.
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- B4 Solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation.
Simultaneous equations