In Exercises 13–15, write each equation in its equivalent exponential form. 1/2 = log49 7

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverse of exponential functions. They express the power to which a base must be raised to obtain a certain number. For example, in the equation log_b(a) = c, b is the base, a is the result, and c is the exponent. Understanding this relationship is crucial for converting between logarithmic and exponential forms.

Exponential Form

Exponential form refers to expressing a number as a base raised to a power. For instance, the equation a = b^c indicates that b is raised to the power of c to yield a. In the context of logarithms, converting a logarithmic equation to exponential form allows us to solve for unknown variables by rewriting the equation in a more straightforward manner.

Change of Base Formula

The change of base formula is a method used to convert logarithms from one base to another, which can simplify calculations. It states that log_b(a) can be expressed as log_k(a) / log_k(b) for any positive k. This concept is particularly useful when dealing with logarithms that do not have a readily available base, allowing for easier computation and understanding of logarithmic relationships.