Logarithms

Logarithms are a branch of calculus. Free Calculus Help offers help with logarithms, help with solving logarithms, tutorials on logarithms, laws of logarithm, logarithm equations, logarithm series, logarithm exponentials, and other properties of logarithms in an effort to help students with understanding logarithms.

Understanding logarithms

A convenient and intuitive way to think about the logarithm function is as the inverse to the exponentiation function. For example, consider

f(x) = 3 ^x

If x = 2 then f(x) = f(2) = 3 x 3 = 9

If x = 3 then f(x) = f(3) = 3 x 3 x 3 = 27

and so on.

What is the logarithm function of f(x)?

The logarithm function of f(x) is the function g(x) where g is the inverse of f. The example of the logarithm function below will make this definition clearer.

From the understanding logarithms example above, for x=2,

f(2) = 9

That means g is the function such that g(9) = 2. In another word,

g(f(x)) = x

g is called the logarithm of function f. Logarithms are usually defined with a base. In this case

f(x) = 3 ^x

Therefore, g is the logarithm to the base 3. We write logarithms to base k as

log _k (x).