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 only support base 10 or base e (the natural logarithm). By using the Change of Base Formula, you can easily switch between different logarithmic bases, making it simpler to solve equations or evaluate logarithmic expressions. This is especially helpful in fields like mathematics, science, and engineering, where logarithms frequently appear in calculations.