In Exercises 81–100, evaluate or simplify each expression without using a calculator. 10^(log 33)

Key Concepts

Exponential and Logarithmic Functions

Exponential functions involve expressions where a constant base is raised to a variable exponent, while logarithmic functions are the inverse operations of exponentials. Understanding the relationship between these two types of functions is crucial for simplifying expressions like 10^(log 33), as it allows us to manipulate the expression using properties of logarithms.

Properties of Logarithms

Logarithms have specific properties that simplify calculations, such as the fact that a^log_a(b) = b for any positive a. This property is essential for evaluating expressions involving logarithms, as it allows us to convert between exponential and logarithmic forms, making it easier to find the value of expressions like 10^(log 33).

Base of a Logarithm

The base of a logarithm indicates the number that is raised to a power to obtain a given value. In the expression log 33, the base is implicitly 10 (common logarithm). Recognizing the base is important for understanding how to evaluate expressions involving logarithms and exponentials, particularly when simplifying expressions like 10^(log 33).