How to Evaluate Logarithms? (+FREE Worksheet!)
Do you want to know how to evaluate Logarithms? You can do it in a few easy steps!
[include_netrun_products_block from-products="product/the-most-comprehensive-ftce-math-preparation-bundle-includes-ftce-math-prep-books-workbooks-and-practice-tests/" product-list-class="bundle-products float-left" product-item-class="float-left" product-item-image-container-class="p-0 float-left" product-item-image-container-size="col-2" product-item-image-container-custom-style="" product-item-container-size="" product-item-add-to-cart-class="btn-accent btn-purchase-ajax" product-item-button-custom-url="{url}/?ajax-add-to-cart={id}" product-item-button-custom-url-if-not-salable="{productUrl} product-item-container-class="" product-item-element-order="image,title,purchase,price" product-item-title-size="" product-item-title-wrapper-size="col-10" product-item-title-tag="h3" product-item-title-class="mt-0" product-item-title-wrapper-class="float-left pr-0" product-item-price-size="" product-item-purchase-size="" product-item-purchase-wrapper-size="" product-item-price-wrapper-class="pr-0 float-left" product-item-price-wrapper-size="col-10" product-item-read-more-text="" product-item-add-to-cart-text="" product-item-add-to-cart-custom-attribute="title='Purchase this book with single click'" product-item-thumbnail-size="290-380" show-details="false" show-excerpt="false" paginate="false" lazy-load="true"]
Related Topics
Step by step guide to Evaluating Logarithms
- Logarithm is another way of writing exponent. \(log_{b}{y}=x\) is equivalent to \(y=b^x \)
- Learn some logarithms rules:
\(log_{b}{(x)}=\frac{log_{d}{(x)}}{\log_{d}{(b)}}\)
\(log_{a}{x^b}=b log_{a}{x}\)
\(log_{a}{1}=0\)
\(log_{a}{a}=1\) For education statistics and research, visit the National Center for Education Statistics.
For education statistics and research, visit the National Center for Education Statistics.
Evaluating logarithms – Example 1:
Evaluate: \(log_{2}{16}\)
Solution:
Rewrite \(16\) in power base form: \(16=2^4\) , then: \(log_{2}{16}=log_{2}{(2^4)}\)
Use log rule: \(log_{a}{x^b}=b log_{a}{x}\), then: \(log_{2}{(2^4)}=4log_{2}{2}\)
Use log rule: \(log_{a}{a}=1\), then: \( 4log_{2}{2}=4\times1=4\)
The Absolute Best Books to Ace Pre-Algebra to Algebra II
Evaluating logarithms – Example 2:
Evaluate: \(log_{6}{216}\)
Solution:
Rewrite \(216\) in power base form: \(216=6^3\) , then: \(log_{6}{216}=log_{6}{(6^3)}\)
Use log rule: \(log_{a}{x^b}=b log_{a}{x}\), then: \(log_{6}{(6^3)}=3 log_{6}{6}\)
Use log rule: \(log_{a}{a}=1\), then: \( 3 log_{6}{6}=3\times1=3\)
Evaluating logarithms – Example 3:
Evaluate: \(log_{4}{64}\)
Solution:
Rewrite \(64\) in power base form: \(64=4^3\) , then: \(log_{4}{64}=log_{4}{(4^3)}\)
Use log rule: \( log_{a}{x^b}=b log_{a}{x}\), then: \(log_{4}{(4^3)}=3 log_{4}{4}\)
Use log rule: \(log_{a}{a}=1\), then: \( 3 log_{4}{4}=3\times1=3\)
The Absolute Best Book to Evaluate Logarithms
Evaluating logarithms – Example 4:
Evaluate: \(log_{5}{625}\)
Solution:
Rewrite \(625\) in power base form: \(625=5^4\) , then: \(log_{5}{625}=log_{5}{(5^4)}\)
Use log rule: \( log_{a}{x^b}=b log_{a}{x}\), then: \(log_{5}{(5^4)}=4 log_{5}{5}\)
Use log rule: \(log_{a}{a}=1\), then: \(4 log_{5}{5}=4\times1=4\)
Evaluating logarithms Exercises
Evaluate each logarithm.
- \(\color{blue}{log_{2}{\frac{1}{2}}}\)
- \(\color{blue}{log_{2}{\frac{1}{8}}}\)
- \(\color{blue}{log_{3}{\frac{1}{3}}}\)
- \(\color{blue}{log_{4}{\frac{1}{16}}}\)
- \(\color{blue}{log_{5}{25}}\)
- \(\color{blue}{log_{3}{27}}\)
- \(\color{blue}{log_{3}{9}}\)
- \(\color{blue}{log_{2}{32}}\)
Answers
- \(\color{blue}{-1}\)
- \(\color{blue}{-3}\)
- \(\color{blue}{-1}\)
- \(\color{blue}{-2}\)
- \(\color{blue}{2}\)
- \(\color{blue}{3}\)
- \(\color{blue}{2}\)
- \(\color{blue}{5}\)
The Greatest Books for Students to Ace the Algebra
Related to This Article
More math articles
- How to Understand Convergent and Divergent Series
- How to Prepare for FTCE General Knowledge Math Test?
- 10 Most Common 5th Grade OST Math Questions
- How to Simplify Variable Expressions? (+FREE Worksheet!)
- The Best Keyboards For Online Teaching
- 10 Most Common 7th Grade PARCC Math Questions
- How to ACE the SAT Math?
- CBEST Math Practice Test Questions
- The Ultimate 7th Grade WVGSA Math Course (+FREE Worksheets)
- Top 10 4th Grade NYSE Math Practice Questions
What people say about "How to Evaluate Logarithms? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.