Use the various properties of exponential and logarithmic functions to evaluate the expressions in parts (a)–(c). Given ƒ(x) = log_2 x, find ƒ(2^(log_2 2))

Key Concepts

Exponential Functions

Exponential functions are mathematical expressions in the form f(x) = a^x, where 'a' is a positive constant and 'x' is the exponent. These functions exhibit rapid growth or decay, depending on the base. Understanding how to manipulate and evaluate exponential expressions is crucial for solving problems involving logarithms, as they are inversely related.

Logarithmic Functions

Logarithmic functions are the inverse of exponential functions, expressed as f(x) = log_a(x), where 'a' is the base. They answer the question: to what exponent must the base 'a' be raised to obtain 'x'? Familiarity with properties of logarithms, such as the product, quotient, and power rules, is essential for simplifying and evaluating logarithmic expressions.

Properties of Logarithms and Exponents

The properties of logarithms and exponents include key rules such as log_a(a^b) = b and a^(log_a(b)) = b. These properties allow for the simplification of complex expressions involving both types of functions. Mastery of these properties is vital for evaluating expressions like ƒ(2^(log_2 2)), as they facilitate the conversion between exponential and logarithmic forms.