Exponential And Logarithmic Functions
Akopọ
Exponential and logarithmic functions sit at the heart of Further Pure Mathematics, connecting algebra, calculus and real-world modelling. Whether you are describing population growth, radioactive decay or compound interest, these two families of functions provide the tools you need.
In this topic you will learn to recognise the shape and behaviour of exponential curves and their inverses, apply the laws of logarithms to simplify and solve equations, and move fluently between exponential and logarithmic forms. Every technique is practised through graded worked examples that mirror the style Edexcel examiners reward.
Awọn Afojusun
- Know the functions a^x and log_b(x) where b is a natural number greater than one, including the shape of their graphs
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Oriire fun ipari ẹkọ lori Exponential And Logarithmic Functions. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
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- What is the value of log_2(32)? A) 4 B) 5 C) 6 D) 8 Answer: B
- The graph of y = 3^x passes through which of these points? A) (0, 0) B) (0, 1) C) (1, 0) D) (0, 3) Answer: B
- Which expression is equivalent to log(a) + log(b)? A) log(a + b) B) log(ab) C) log(a) x log(b) D) log(a^b) Answer: B
- What is the vertical asymptote of the graph y = log_5(x)? A) y = 0 B) x = 1 C) x = 0 D) y = 1 Answer: C
- If 4^x = 64, what is the value of x? A) 2 B) 3 C) 4 D) 16 Answer: B
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Awọn Iwe Itọsọna Ti a Gba Nimọran
Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
Graphs of Exponential Functions
Graph exponential functions.
"Algebra and Trigonometry: Graphs of Exponential Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/6-2-graphs-of-exponential-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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Abala ìwé ẹ̀kọ́
Logarithmic Functions
Convert from logarithmic to exponential form.
"College Algebra: Logarithmic Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/6-3-logarithmic-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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