Properties Of Logarithmic Functions Math

An exponential function is a function of the form f x bx where b 0 and x is any real number.

Properties of logarithmic functions math. If b b is any number such that b 0 b 0 and b 1 b 1 and x 0 x 0 then y logbx is equivalent to by x y log b x is equivalent to b y x. The logarithmic function is defined as. The most 2 common bases used in logarithmic functions are base 10 and base e. Properties of logarithmic functions.

In mathematics the logarithmic function is an inverse function to exponentiation. The point of math is to understand math so you can actually apply it in life later on and not have to relearn everything every time. Logb x y means that x bywhere x 0 b 0 b 1. The logarithms of a positive number to the base of the same number is equal to 1.

So the next logarithm property is if i have a times the logarithm base b of c if i have a times this whole thing that that equals logarithm base b of c to the a power. The bases of an exponential function and its equivalent logarithmic function are equal. So that s important to remember. That equals the logarithm of base b of a times c.

Logarithm base b of a plus logarithm base b of c and this only works if we have the same bases. We usually read this as log base b b of x x. Other properties of logarithmic functions include. Then the function is given by.

In this definition y logbx y log b x is called the logarithm form and by x b y x is called the exponential form. Note that f x x2is not an exponential function logarithmic functions. Log a a 1. This can be read it as log base a of x.

The logarithmic function of base a where a is positive and not 1 is denoted by which is read as y is log base a of x and is defined by properties domain of logarithmic function range of exponential function 0 displaystyle 0 infty range of logarithmic function domain of exponential function. The logarithm let s say of any base so let s just call the base let s say b for base.