Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

In ALEKS, what topic might involve solving for x in logarithmic functions?

1. Polynomial functions

2. Exponential functions and their inverses

3. Linear equations

4. Basic arithmetic operations

The correct answer is: Exponential functions and their inverses

The correct answer is focused on exponential functions and their inverses because logarithmic functions are intricately linked to exponential functions. In mathematics, a logarithm is defined as the inverse operation to exponentiation. This means that solving for x in logarithmic equations often involves transforming the logarithmic equation into an exponential form to isolate x. For example, if you have a logarithmic equation like log_b(x) = y, you can rewrite it as x = b^y. Understanding this relationship allows one to solve for x effectively when dealing with logarithmic functions. The topic covers necessary skills for dealing with equations where x is an unknown in logarithmic forms and illustrates how logarithms can be applied in various contexts, such as in growth and decay problems. In contrast, polynomial functions, linear equations, and basic arithmetic operations do not inherently involve logarithmic equations, making them less relevant to the context of solving for x in logarithmic functions.