Definition Of Log Function Math

Here is the definition of the logarithm function.

Definition of log function math. The most 2 common bases used in logarithmic functions are base 10 and base e. 2 2 2 8 so we had to multiply 3 of the 2s to get 8. When b is raised to the power of y is equal x. 8 2 3 answer.

This can be read it as log base a of x. A function such as y loga x or y ln x that is the inverse of an exponential function such as y ax or y ex so that the independent variable appears in a logarithm. For example the base ten logarithm of 100 is 2 because ten raised to the power of two is 100. Properties depend on value of a.

A logarithm is the power to which a number must be raised in order to get some other number see section 3 of this math review for more about exponents. This is the logarithmic function. The 2 most common bases that we use are base 10 and base e which we meet in logs to base 10 and natural logs base e in later sections. Write in logarithm form.

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 we usually read this as log base b b of x x. The logarithmic function has many real life applications in acoustics electronics earthquake analysis and population prediction. F x log a x. Then the function is given by.

Definition of logarithmic function. A is any value greater than 0 except 1. The logarithmic function is defined as. 2 4 16.

Log 2 16 4. The logarithmic function y log b x is the inverse function of the. F x log a x. The base of the logarithm is a.

F x log b x the base of the logarithm is b. For x 0 a 0 and a neq 1 y log a x if and only if x a y. 10 2 100. The function that assigns to y its logarithm is called logarithm function or logarithmic function or just logarithm.

In mathematics the logarithmic function is an inverse function to exponentiation. Then the base b logarithm of x is equal to y. A logarithm answers the question how many of this number do we multiply to get that number example how many 2s must we multiply to get 8. Log 100 2.

Log b x y. The function log b x is essentially characterized by the product formula log b x y log b x log b y. B y x.