exponential/logarithmic functions

Exponential functions

Let b > 0, b does not equal 1. Then f(x) = b^x defines an exponential function for each different constant b, called the base. The domain of f is the set of all real numbers. The range of f is the set of all positive real numbers.

Logarithmic Function

a function of the form f(x)=log^bX, where b≠1 and b>0, which is the inverse of the exponential function f(x)=b^X.

base b

Since f(x) = b^x is one to one, it has an inverse. F^-1(x)= log\/bx, called logarithmic function with base b.

base e

The mathematical constant e is the unique real number such that the value of the derivative (slope of the tangent line) of the function f(x) = ex at the point x = 0 is equal to 1.[1] The function ex so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base e.

exponential growth

growth in which some quantity increases at a constant rate per unit of time.

exponential decay

When a>0 and 0

common logarithm

Log base 10 (10 to the exponent)

log x=k only if x=10^k

Change of base formula

Log\/a x= (log\/bx)/(log\/a)

natural base exponential function

An exponential function with the base e, y=e^x.

natural logarithm

ln x=c means that e^c=x and (x>0).