A root is a value (X) that when multiplied by itself (n) number of times provides another value (Y), i.e., Xⁿ=Y. In this exponential equation, X is called a root of Y, n is called the exponent, and Y is called a power of X.

For example, if X=3 and n=2, the equation becomes 3²=9. In this case, 9 is the second power of 3 and 3 is the square root of 9. Written another way, this becomes 9=3 or 9^½=3. Of course, -3 is also a root of 9 because -3^²=9. In practice, an equation written as 9 refers only to the positive root 3 (which is called the principal root), whereas an equation written as ±9 refers to positive and negative roots, i.e., 3 and -3.

Logarithms are used as an aid in simplifying expressions for extracting roots and expanding powers. For the case above...