The exponential function, logarithms or trigonometric functions are functions whereas a complex variable is an element of the complex field.
Each one of the functions can be defined for a complex variable.
The logarithm function. If you specifically mean the function ex, the inverse function is the natural logarithm. However, functions with bases other than "e" might also be called exponential functions.
http://www.wolframalpha.com/input/?i=integrate+exp(x^2) The solution lists an "imaginary error function". This means that the integral can NOT be expressed as a finite number of the so-called elementary functions (that is, as any combination of addition, subtraction, multiplication, division, trigonometric functions, inverse trigonometric functions, exponential function, natural logarithm). The site mentioned also shows a series expansion.
From Wikipedia: "Typical operations are addition, subtraction, multiplication, division, and square root. Some [older] systems ... can also perform various transcendental functions such as exponential or trigonometric calculations, though in most modern processors these are done with software library routines." Trigonometric refers to sine, cosine, etc., as well as the corresponding inverse functions. The exponential function is to calculate ex, in combination with the natural (base e) logarithm, this can be used to calculate powers.
A logarithm can not be converted in to an exponential, as an exponential is defined for all real numbers, while a logarithm is only defined for numbers greater than zero. However, a logarithm can be related to an exponential by the fact that they are inverses of each other. e.g. if y = 2^x the x = log2y
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
The logarithm function. If you specifically mean the function ex, the inverse function is the natural logarithm. However, functions with bases other than "e" might also be called exponential functions.
http://www.wolframalpha.com/input/?i=integrate+exp(x^2) The solution lists an "imaginary error function". This means that the integral can NOT be expressed as a finite number of the so-called elementary functions (that is, as any combination of addition, subtraction, multiplication, division, trigonometric functions, inverse trigonometric functions, exponential function, natural logarithm). The site mentioned also shows a series expansion.
From Wikipedia: "Typical operations are addition, subtraction, multiplication, division, and square root. Some [older] systems ... can also perform various transcendental functions such as exponential or trigonometric calculations, though in most modern processors these are done with software library routines." Trigonometric refers to sine, cosine, etc., as well as the corresponding inverse functions. The exponential function is to calculate ex, in combination with the natural (base e) logarithm, this can be used to calculate powers.
A logarithm can not be converted in to an exponential, as an exponential is defined for all real numbers, while a logarithm is only defined for numbers greater than zero. However, a logarithm can be related to an exponential by the fact that they are inverses of each other. e.g. if y = 2^x the x = log2y
Domain of the logarithm function is the positive real numbers. Domain of exponential function is the real numbers.
The inverse function of the exponential is the logarithm.
The number "e" is a mathematical constant that is approximately equal to 2.71828. It is the base of the natural logarithm and appears in many areas of mathematics, particularly in calculus and exponential functions.
My daughter's math teacher recommended the following site, which was enormously helpful for her. Here's a link to the 'natural logarithm' topic, and you can find a bunch of other math topic videos there. It is all free. Hope it will help.http://www.brightstorm.com/d/math/s/precalculus/u/exponential-and-logarithmic-functions/t/the-number-e-and-the-natural-logarithm
You must remember that complex numbers need two parts - a real and an imaginar part, so you have to define fields for these parts. You also need to define methods at least for the basic operations, such as addition, subtraction, multiplication and division. You may also want to define methods for more advanced operations, such as trigonometric functions and the exponential function and natural logarithm, all of which have special definitions in the case of complex numbers.
The exponential function, in the case of the natural exponential is f(x) = ex, where e is approximately 2.71828. The logarithmic function is the inverse of the exponential function. If we're talking about the natural logarithm (LN), then y = LN(x), is the same as sayinig x = ey.
logb x = a According to the definition of the logarithm, a is the number that you have to exponentiate b with to get x as a result. Therefore: ba = x
A logarithm is the exponent to which a number called a base is raised to become a different specific number. A common logarithm uses 10 as the base and a natural logarithm uses the number e (approximately 2.71828) as the base.