Properties of Logarithms

Properties of Logarithms

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

Step by step guide to Properties of Logarithms

Learn some logarithms properties:

  • \(a^{\log_{a}{b}}=b\)
  • \(\log_{a}{1}=0\)
  • \(\log_{a}{a}=1\)
  • \(\log_{a}{x.y}=\log_{a}{x}+\log_{a}{y}\)
  • \(\log_{a}{\frac{x}{y}}=\log_{a}{x}-\log_{a}{y}\)
  • \(\log_{a}{\frac{1}{x}}=-\log_{a}{x}\)
  • \(\log_{a}{x^p}=p\log_{a}{x}\)
  • \(\log_{x^k}{x}=\frac{1}{x}\log_{a}{x}, for k\neq0\)
  • \(\log_{a}{x}=\log_{a^c}{x^c}\)
  • \(\log_{a}{x}=\frac{1}{\log_{x}{a}}\)

Example 1:

Expand this logarithm. \(log ⁡(8×5)=\)

Solution:

Use log rule: \(\log_{a}{x.y}=\log_{a}{x}+\log_{a}{y}\)

then: \(log ⁡(8×5)= log 8 + log 5\)

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: \(log 2-log 9= \log{\frac{2}{9}}\)

Example 3:

Expand this logarithm. \(log ⁡(2×3)=\)

Solution:

Use log rule: \(\log_{a}{x.y}=\log_{a}{x}+\log_{a}{y}\)

then: \(log ⁡(2×3)= log 2 + log 3\)

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

Expand each logarithm.

  1. \(log ⁡(8×5)=\)
  2. \(log ⁡(9×4)=\)
  3. \(log ⁡(3×7)=\)
  4. \( \log{\frac{3}{4}}\)
  5. \( \log{\frac{5}{7}}\)
  6. \( \log({\frac{2}{5}})^3\)
  7. \(log ⁡(2×3^4)=\)
  8. \( \log({\frac{5}{7}})^4\)

Answers

  1. \(log 8+log 5\)
  2. \( log 9+log 9\)
  3. \( log 3+log 7\)
  4. \( log 3-log 4\)
  5. \( log 5-log 7\)
  6. \(3 log 2-3 log 5\)
  7. \(log 2+4 log 3\)
  8. \(4log 5-4 log 7\)

Related to "Properties of Logarithms"

FREE Grade 7 PARCC Math Practice Test
FREE Grade 7 PARCC Math Practice Test
Grade 6 STAAR Math Worksheets
Grade 6 STAAR Math Worksheets
Top 10 Grade 7 ACT Aspire Math Practice Questions
Top 10 Grade 7 ACT Aspire Math Practice Questions
TExES Core Math FREE Sample Practice Questions
TExES Core Math FREE Sample Practice Questions
Grade 6 PSSA Math Worksheets
Grade 6 PSSA Math Worksheets
FREE Grade 7 SBAC Math Practice Test
FREE Grade 7 SBAC Math Practice Test
ATI TEAS 6 Math Practice Test Questions
ATI TEAS 6 Math Practice Test Questions
Top 10 Grade 8 Georgia Milestones Assessment System Math Practice Questions
Top 10 Grade 8 Georgia Milestones Assessment System Math Practice Questions
SHSAT Math FREE Sample Practice Questions
SHSAT Math FREE Sample Practice Questions
Grade 6 MCAS Math Worksheets
Grade 6 MCAS Math Worksheets

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…