logb1xy

logb1xy is a mathematical expression involving logarithms. It represents the logarithm of the product of two variables, x and y, to the base b.

In mathematics, a logarithm answers the question of how many times a base number must be multiplied by itself to reach a certain number. The expression logb(a) means "the power to which b must be raised to get a".

Therefore, logb(xy) can be expanded using the properties of logarithms. One of the fundamental properties of logarithms is the product rule, which states that the logarithm of a product is equal to the sum of the logarithms of the factors. Applying this rule to logb(xy), we get:

logb(xy) = logb(x) + logb(y)

This identity is extremely useful in simplifying logarithmic expressions and solving logarithmic equations. For this expression to be defined, the base b must be a positive real number other than 1. Additionally, both x and y must be positive real numbers, as the logarithm of a non-positive number is not defined in the real number system. The value of logb(1xy) depends on the specific values of b, x, and y.