The Change of Base Formula is a mathematical tool used to convert logarithms from one base to another. It states that for any positive numbers a , b , and x (where a ≠ 1 and b ≠ 1 ), the logarithm can be expressed as: \[ \log_b(x) = \frac\log_a(x)\log_a(b) \] This formula is particularly useful when calculating logarithms on calculators that typically only support base 10 (common logarithm) or base e (natural logarithm). By using the Change of Base Formula, you can easily switch between bases, making it simpler to solve problems in various fields such as mathematics, science, and engineering. This flexibility allows for easier computation and understanding of logarithmic relationships.