In mathematics, the exponential function is the function ex, where e is the number (approximately 2.718281828) such that the function ex equals its own derivative. The exponential function is used to model phenomena when a constant change in the independent variable gives the same proportional change (increase or decrease) in the dependent variable. The exponential function is often written as exp(x), especially when the input is an expression too complex to be written as an exponent. (Source: From Wikipedia)
The inverse exponential function is in the form of 1/ ex . Logarithmic functions are inverse of exponential functions.
Inverse of exponential function and rules:
Inverse of exponential function:
A function f may have the same value for difference numbers in its domain. Example, if f(x) = x^2, then f (2) = 4 and f (-2) = 4, but 2 ≠ -2. For the inverse of a function to be essential that different numbers in the domain always give different value of f.
General logarithm function:
y = log a x , where a = base, a>0 and a and x = variable which takes values x >0. If the base of a logarithm function is not specified, Then the base of the function is considered to be 10.
Natural logarithmic function:
f (x) = ln x is the natural exponential function,
f- -1(x) = ex
y = ex if and only if x = ln y
y = ln x, here base is e
Rules of Exponentiation:
The rules used in manipulate exponential functions are:
* bx+y =...