If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log￬4 1/64 = -3

Key Concepts

Exponential and Logarithmic Functions

Exponential functions are mathematical expressions where a constant base is raised to a variable exponent, while logarithmic functions are the inverse operations of exponentials. For example, if b^y = x, then log_b(x) = y. Understanding the relationship between these two forms is crucial for converting between them.

Change of Base Formula

The change of base formula allows you to convert logarithms from one base to another, which can be useful for calculations. It states that log_b(a) = log_k(a) / log_k(b) for any positive k. This concept is important when dealing with logarithmic expressions that may not be in a familiar base.

Properties of Logarithms

Logarithms have several key properties that simplify calculations, such as the product, quotient, and power rules. For instance, log_b(mn) = log_b(m) + log_b(n) and log_b(m/n) = log_b(m) - log_b(n). Familiarity with these properties aids in manipulating logarithmic expressions effectively.