Definition Logarithm Exponential Function

We can write this equation in logarithm form with identical meaning as follows.

Definition logarithm exponential function. We can never take the logarithm of a negative number therefore logb x y l o g b x y is defined for b 0 b 0. The logarithmic function y log a x is defined to be equivalent to the exponential equation x a y. An exponential function is the inverse of a logarithm function. Y b x.

X a y. It is called the logarithmic function with base a. Corresponding to every logarithm function with base b we see that there is an exponential function with base b. Log 3 9 2.

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y a x is x a y. Log b y x means b x y. Logarithmic functions are the inverse of exponential functions and it is often easier to understand them through this lens.

3 2 9 in this case the base is 3 and the exponent is 2. We will go into that more below. A logarithm is simply an exponent that is written in a special way. In order to solve equations that contain exponentials we need logarithmic functions.

The properties of logarithms are used frequently to help us simplify exponential functions. An exponential function is defined for every real number x. Logarithmic functions are the inverses of exponential functions. Y log a x only under the following conditions.

X a y a 0 and a 1.