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Property of Equality for Logarithmic Equations

Rule

Property of Equality for Logarithmic Equations

The Property of Equality for Logarithmic Equations states that if two logarithms with the same base are equal, then the logarithms' arguments must be equal.

$lo g_{b} (x) = lo g_{b} (y) \Leftrightarrow x = y$

This identity is true if $x,$ $y,$ and $b$ all are positive real numbers and $b \neq = 1 .$