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Logarithmic form is the representation of a formula in terms of Logarithmic function. It is just the opposite of exponential form . It can varies from the simpliest case of rewriting a mathematical formula, to the conversion of complex exponential functions into logarithmic forms. In short:- if the exponential form is: , then
- the logarithmic form is:
The logarithmic form is useful when we need to solve a problem in a particular way, or we need to write our answer in a elegant way. For example, the general formula of the integration result of is |log u| + C.
1 Number theory
In number theory a logarithmic form or linear form in logarithms is assumed to be a finite sum
- Σ αi log βi = Λ
where the αi and βi are algebraic numbers. In case of βi a complex number, one has to allow log to denote some definite branch of the logarithm function in the complex plane. The basic problem attacked in Alan Baker's work is to supply lower bounds for |Λ|, in cases where Λ ≠ 0. This is in terms of quantities A and B, repectively bounding the heights of the αi and βi. This work supplied many results on diophantine equations, amongst other applications. It has been suitably generalised to abelian varieties.
2 External links
