Evaluate the given logarithmic expression. l o g 10 0.1 log_{10}0.1

we're asked to evaluate the given logarithmic expression log base 10 of 0.1. So here we wanna be thinking, what power can I raise that base of 10 to in order to get that argument 0.1? Now this might seem a little bit confusing that we're looking for a decimal here, but we can make this a bit easier by thinking about this decimal instead as a fraction. 0.1 is the same thing as the fraction one tenth. So now if we think about what power we need to raise 10 to in order to get one tenth, this might seem a bit easier. Because if I take 10 and raise it to the power of negative one, that will flip it to the bottom of a fraction and give me one tenth, which is exactly what I'm looking for. So that tells me that log base 10 of 0.1 is equal to the exponent negative one. Let us know if you have questions and we'll keep working with logs coming up soon.

Table of contents

Skip topic navigation

1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving43m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
21m

Translating Sentences to Algebraic Equations
2m

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics40m

Tables
12m

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
14m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
38m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

Ellipses
35m

Hyperbolas
41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

20. Exponential and Logarithmic Functions

Introduction to Logarithmic Functions

Prealgebra, Beginning Algebra, & Intermediate Algebra

20. Exponential and Logarithmic Functions

Introduction to Logarithmic Functions

Previous problemNext problem

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Evaluate the given logarithmic expression.
$l o g sub 10 of 0.1$

$-1$

$1$

$-0.1$

$10$

0 Comments

Previous problemNext problem

6:06m

Watch next

Master Intro to Logarithms with a bite sized video explanation from Patrick Ford

Struggling with Prealgebra, Beginning Algebra, & Intermediate Algebra?

Evaluate the given logarithmic expression.log100.1log_{10}0.1

Watch next

Evaluate the given logarithmic expression.
$l o g sub 10 of 0.1$