Tutorials > Exponents & Radicals

# Introduction to Exponents & Radicals

## Exponents

An exponent is shorthand for the amount of times a number is multiplied by itself. Exponent may also be called the "power" or "index." For example 4 x 4 x 4 could be rewritten as 4^3 or "4 to-the-third power." In this case 3 is the "exponent" and 4 is referred to as the "base."

An exponent of 2 is often referred to as "squared." For example 4^2 would commonly be referred to as "4-squared," but it could also be called "4 to the power of 2" or "4 to the second power."

## Logarithms

Logarithms ask how many times must a given number be multiplied by itself to give us another given number. In other words given a number (called our "base), what exponent would produce a given answer.

For example, we might ask "what exponent of 4 produces the number 64?" or we could write log4(64). We know 4 multiplied by itself 3 times = 64 (4 x 4 x 4 = 64). So the answer to log4(64) = 3.

A logarithm with a base of 10 is called a "common logarithm." It is often written without a base. For example log10(x) is commonly written as log(x).

A logarithm with a base of e ("Euler's Number" = 2.718281828459...) is called a "natural logarithm." Instead of being written as loge(x) it is more commonly written as ln(x)

## Radicals

Coming soon!