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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1:01 minutes

Problem 88

Textbook Question

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

Verified step by step guidance

Identify the type of expression given in the exercise (e.g., polynomial, rational, radical, etc.).

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

Apply any relevant algebraic rules or properties, such as the distributive property, to simplify the expression.

If the expression involves fractions, find a common denominator to combine them if necessary.

Check if the expression can be further simplified or if it is in its simplest form.

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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.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations that represent a value. They can include constants, coefficients, and various mathematical operations. Understanding how to manipulate these expressions, such as combining like terms and applying distributive properties, is essential for evaluating or simplifying them.

Factoring

Factoring is the process of breaking down an expression into its constituent parts or factors that, when multiplied together, yield the original expression. This concept is vital for simplifying expressions and solving equations, as it can reveal solutions or make calculations easier. Common techniques include factoring out the greatest common factor and using special products.