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

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions. The logarithm log_b(a) answers the question: 'To what exponent must the base b be raised to produce a?' Understanding logarithms is crucial for simplifying expressions involving exponents, as they allow us to manipulate and solve equations involving powers.

Properties of Logarithms

Properties of logarithms, such as the power rule, product rule, and quotient rule, provide essential tools for simplifying logarithmic expressions. For instance, the power rule states that log_b(a^c) = c * log_b(a), which is particularly useful when dealing with roots and exponents in logarithmic expressions.

Exponential and Logarithmic Relationships

The relationship between exponential functions and logarithms is foundational in algebra. Specifically, if y = b^x, then x = log_b(y). This relationship allows us to convert between exponential and logarithmic forms, which is key to evaluating expressions like 10^(log ∛x) by recognizing that it can be simplified using the properties of logarithms.