Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

6. Exponential & Logarithmic Functions

Introduction to Logarithms

College Algebra

6. Exponential & Logarithmic Functions

Introduction to Logarithms

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0:48 minutes

Problem 87

Textbook Question

In Exercises 81–100, evaluate or simplify each expression without using a calculator. In 1

Verified step by step guidance

Identify the expression that needs to be evaluated or simplified.

Determine if there are any algebraic operations or simplifications that can be applied, such as combining like terms or factoring.

Look for any special algebraic identities or formulas that might apply to the expression.

Apply the appropriate algebraic rules or identities to simplify the expression step by step.

Verify that the expression is fully simplified and check for any possible errors in the simplification process.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. Following these rules is crucial when simplifying expressions to avoid errors.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form by combining like terms, eliminating parentheses, and performing operations. This process often includes factoring, distributing, and applying the order of operations. Mastery of simplification is essential for solving equations and evaluating expressions accurately.

Evaluating Expressions

Evaluating expressions means substituting variables with their respective values and performing the necessary calculations to find a numerical result. This process requires a solid understanding of arithmetic operations and the ability to apply the order of operations correctly. It is a fundamental skill in algebra that allows students to solve problems and analyze mathematical relationships.