The Property of Inequality for Logarithmic Equations states that if two common logarithms form an inequality, the inequality also holds true for the logarithms' arguments.

This identity is true if $x$ and $y$ are positive real numbers. The same relation holds true for any logarithm with a base $b$ greater than $1.$ However, if the base, $b,$ of the logarithm is less than $1,$ the opposite is true.