Properties of Logarithms

In this section, we continue to learn about logarithms. Specifically, we will focus on a few key properties. The first property is known as the product rule for logarithms. This property tells us the logarithm of a product is the sum of the logarithms of the factors. Next, we encounter the quotient rule for logarithms. This property tells us that the logarithm of a quotient is the difference between the logarithm of the numerator and the logarithm of the denominator. We then move into a section where we discuss the power rule for logarithms. This rule tells us the logarithm of a number to a power equals the exponent multiplied by the logarithm of the number. Lastly, we will encounter two special properties. First, if we take b to the power of log base b of x, the result will be x (for b > 0, & b ≠ 1 & x > 0). Second, if we have log base b of b to the power of x, the result will be x (for b > 0, and b ≠ 1).