A common base refers to the shared base in exponential and logarithmic equations that allows for simplification and solving. It is often used to compare, combine, or solve exponential expressions by rewriting them with the same base.
Exponential Function: A function of the form $f(x) = a \cdot b^x$ where $b > 0$ and $b \neq 1$.
Logarithm: The inverse operation to exponentiation, denoted as $\log_b(x)$ meaning the power to which the base $b$ must be raised to yield $x$.
Change of Base Formula: $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$, which allows conversion between different logarithmic bases.