Karteikarten
Exponentials and Logarithms
Karten in diesem Stapel (10)
- 1What are exponentials/indices?Powers, ie. \(x^n\) = \(x\) multiplied by itself \(n\) times
- 2What are logarithms?Inverse of exponentiation (ish)
Used to find the index/exponent ( \(n\) in \(x^n\))
e.g. \(\log_{a}{a^b} = b\) - 3What are the laws of indices?\(x^a \times x^b = x^{a + b}\)
\(\frac{x^a}{x^b} = x^{a - b}\)
\((x^a)^b = x^{ab}\)
\(\sqrt[a]{x} = x^{\frac{1}{a}}\)
\(\frac{1}{x^a} = x^{-a}\) - 4What are the laws of logarithms?\(\log_{a}{bc} = \log_{a}b + \log_{a}c\)
\(\log_{a}{b^c} = c\log_{a}b\)
\(\frac{\log_{a}b}{\log_{a}c}=log_{c}a\)
\(\log_{a}a = 1\)
\(\log_{a}1 = 0\)
You cannot log a negative number to any base! - 5How can exponential and polynomial relationships be modelled in a linear fashion?Take logarithms to both sides
- 6Model the polynomial relationship \(y = ax^n\) in a linear fashion\(y = ax^n\)
\(\ln{y} = \ln{ax^n}\)
\(ln{y} = \ln{a} + n\ln{x}\) - 7Model the exponential relationship \(y = ar^x\) in a linear fashion\(y = ar^x\)
\(\ln{y} = \ln{ar^x}\)
\(ln{y} = \ln{a} + x\ln{r}\) - 8Solving equations involving logarithmsTake appropriate logarithms to both sides then rearrange
- 9Types of equations involving logarithms\(a^x=b\)
\(a^x=b^x\)
\(a^{2x} + b = a^x + c\)
Or variations thereupon - 10Solving inequalitiesDo not take logarithms to one of the bases
Use base 10 or base \(e\)
Informationen
- Beschreibung
- A level OCR A level Maths (Algebra) Karteikarten am Exponentials and Logarithms, erstellt von James Norman am 30/12/2018.
- Erstellt von
- James Norman
- Aufrufe
- 2
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