Properties of Logarithms
Do you want to know how to Properties of Logarithms? you can do it in two easy steps.

Related Topics
- How to Solve Logarithmic Equations
- How to Solve Natural Logarithms Problems
- How to Evaluate Logarithms
Properties of Logarithms
Learn some logarithms properties:
- \(a^{log_{a}{b}}=b\)
- \(log_{a}{1}=0\)
- \(log_{a}{a}=1\)
- \(log_{a}{x.y}=log_{a}{x}+\log_{a}{y}\)
- \(log_{a}{\frac{x}{y}}=log_{a}{x}-\log_{a}{y}\)
- \(log_{a}{\frac{1}{x}}=-log_{a}{x}\)
- \(log_{a}{x^p}=p log_{a}{x}\)
- \(log_{x^k}{x}=\frac{1}{x}log_{a}{x}\), for \(k\neq0\)
- \(log_{a}{x}= log_{a^c}{x^c}\)
- \(log_{a}{x}=\frac{1}{log_{x}{a}}\)
Logarithms Properties – Example 1:
Expand this logarithm. \(log (8×5)=\)
Solution:
Use log rule: \(log_{a}{x.y}=log_{a}{x}+\log_{a}{y}\)
then: \(log (8×5)= log 8 + log 5\)
Logarithms Properties – Example 2:
Condense this expression to a single logarithm. \(log 2-log 9=\)
Solution:
Use log rule: \(log_{a}{\frac{x}{y}}=log_{a}{x}-\log_{a}{y}\)
then: \(log 2-log 9= log{\frac{2}{9}}\)
Logarithms Properties – Example 3:
Expand this logarithm. \(log (2×3)=\)
Solution:
Use log rule: \(log_{a}{x.y}=log_{a}{x}+\log_{a}{y}\)
then: \(log (2×3)= log 2 + log 3\)
Logarithms Properties – Example 4:
Condense this expression to a single logarithm. \(log 4-log 3=\)
Solution:
Use log rule: \(log_{a}{\frac{x}{y}}=log_{a}{x}-log_{a}{y}\)
then: \(log 4-log 3= log{\frac{4}{3}}\)
Exercises for Logarithms Properties
Expand each logarithm.
- \(\color{blue}{log (12×6)=}\)
- \(\color{blue}{log (9×4)=}\)
- \(\color{blue}{log (3×7)=}\)
- \(\color{blue}{log{\frac{3}{4}}}\)
- \(\color{blue}{log{\frac{5}{7}}}\)
- \(\color{blue}{log({\frac{2}{5}})^3}\)
- \(\color{blue}{log (2×3^4)=}\)
- \(\color{blue}{ log({\frac{5}{7}})^4}\)

Answers
- \(\color{blue}{log 12+log 6}\)
- \(\color{blue}{ log 9+log 4}\)
- \(\color{blue}{log 3+log 7}\)
- \(\color{blue}{ log 3-log 4}\)
- \(\color{blue}{ log 5-log 7}\)
- \(\color{blue}{3 log 2-3 log 5}\)
- \(\color{blue}{log 2+4 log 3}\)
- \(\color{blue}{4log 5-4 log 7}\)
More math articles
- SSAT Middle-Level Math Worksheets: FREE & Printable
- 8th Grade MCAS Math Worksheets: FREE & Printable
- Algebra Puzzle – Challenge 51
- How to Find the Focus, Vertex, and Directrix of a Parabola?
- Algebra Puzzle – Challenge 36
- How to Solve Radicals? (+FREE Worksheet!)
- Are knowledge checks mandatory on ALEKS? 
- Best tools for Online teachers
- FREE 6th Grade OST Math Practice Test
- GED Testing Accommodations and Support for Students with Disabilities
What people say about "Properties of Logarithms"?
No one replied yet.