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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1:49 minutes

Problem 1

Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16

Verified step by step guidance

Understand that the equation given is in logarithmic form: $4 = \log_2 16$.

Recall the definition of a logarithm: $\log_b a = c$ means $b^c = a$.

Identify the base $b$, the result $a$, and the exponent $c$ from the logarithmic equation: here, $b = 2$, $a = 16$, and $c = 4$.

Rewrite the equation in exponential form using the identified values: $2^4 = 16$.

Verify the conversion by calculating $2^4$ to ensure it equals 16, confirming the exponential form is correct.

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Key Concepts

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

Logarithms

Logarithms are the inverse operations of exponentiation. The logarithm log_b(a) answers the question: 'To what exponent must the base b be raised to produce a?' In the given equation, log₂ 16 indicates the power to which 2 must be raised to yield 16.

Exponential Form

Exponential form expresses a logarithmic equation as an exponent. For example, the equation log_b(a) = c can be rewritten in exponential form as b^c = a. This transformation is essential for solving logarithmic equations and understanding their relationships with exponential functions.

Base of a Logarithm

The base of a logarithm is the number that is raised to a power to obtain a given value. In the expression log₂ 16, the base is 2. Understanding the base is crucial for converting logarithmic expressions into their exponential counterparts, as it determines the relationship between the logarithm and the exponent.