What Are Logarithmic Functions? Much before calculus, mathematicians used logarithmic functions to help them with complicated math problems. Like calculus, this form of math helped mathematicians in converting multiplication problems into addition and subtraction problems. Even today, scientists and mathematicians must encounter problems with large powers and complicated multiplications. This is where they are helpful. In mathematics, a logarithmic function is defined as the inverse of the exponential function. Any exponential function can be easily expressed in this format. Similarly, they can be expressed as an exponential form. They allow us to work with large numbers, especially those with large powers. They can be expressed as: For x > 0, a > 0, and a ≠1, y = log a x if and only if x = a y. Then the function is shown as f(x)= log a x. 'a' is the base. This is usually read as the log of base a of x. This form of expression commonly has two types of bases, which are base e and base 10. There is a form that has base 10 is known as the common logarithmic function. It is denoted by log 10 or is simply known as log f(x)= log 10 x. Those that follow this form that have a base 'e' is termed as a natural logarithmic function. It is denoted by log e, f(x)= log e x.

When we are working with very large numbers logarithms come in very handy. They kind of make it like shorthand for extremely large or small values. You will also see the word logarithm listed as log, they are one and the same. In this section we will evaluate logarithm functions and work on converting their values and determining domains of these functions. These worksheets explain how to solve for various log based expressions. They will evaluate and create their own functions.