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

Previous problemNext problem

1:49 minutes

Problem 3

Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 2 = log3 x

Verified step by step guidance

Understand that the given equation is in logarithmic form: $2 = \log_3 x$.

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

Identify the base $b$, the exponent $c$, and the result $a$ from the logarithmic equation: here, $b = 3$, $c = 2$, and $a = x$.

Rewrite the equation in exponential form using the identified components: $3^2 = x$.

Verify the conversion by checking that the exponential form correctly represents the original logarithmic equation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

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?' In the given equation, log3(x) indicates that 3 must be raised to a certain power to yield x.

Exponential Form

Exponential form expresses equations in terms of exponents. For a logarithmic equation like log_b(a) = c, the equivalent exponential form is b^c = a. This transformation is crucial for solving equations involving logarithms, as it allows for easier manipulation and understanding of the relationship between the variables.

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 equation log3(x), the base is 3. Understanding the base is essential for converting logarithmic equations to exponential form, as it determines the relationship between the logarithm and the resulting exponential expression.