How to Evaluate Logarithm? (+FREE Worksheet!)
Since learning the rules of logarithms is essential for evaluating logarithms, this blog post will teach you some logarithmic rules for the convenience of your work in evaluating logarithms.
Related Topics
- How to Solve Natural Logarithms
- How to Use Properties of Logarithms
- How to Solve Logarithmic Equations
Necessary Logarithms Rules
- Logarithm is another way of writing exponent. \(\log_{b}{y}=x\) is equivalent to \(y=b^x\).
- Learn some logarithms rules: \((a>0,a≠0,M>0,N>0\), and k is a real number.)
Rule 1: \(\log_{a}{M.N} =\log_{a}{M} +\log_{a}{N}\)
Rule 2: \(\log_{a}{\frac{M}{N}}=\log_{a}{M} -\log_{a}{N} \)
Rule 3: \(\log_{a}{(M)^k} =k\log_{a}{M}\)
Rule 4: \(\log_{a}{a}=1\)
Rule 5:\(\log_{a}{1}=0\)
Rule 6: \(a^{\log_{a}{k}}=k\)
Examples
Evaluating Logarithm – Example 1:
Evaluate: \(\log_{2}{32}\)
Solution:
Rewrite \(32\) in power base form: \(32=2^5\), then:
\(\log_{2}{32}=\log_{2}{(2)^5}\)
Use log rule:\(\log_{a}{(M)^{k}}=k.\log_{a}{M}→\log_{2}{(2)^5}=5\log_{2}{(2)}\)
Use log rule: \(\log_{a}{(a)}=1→\log_{2}{(2)} =1.\)
\(5\log_{2}{(2)}=5×1=5\)
Evaluating Logarithm – Example 2:
Evaluate: \(3\log_{5}{125}\)
Solution:
Rewrite \(125\) in power base form: \(125=5^3\), then:
\(\log_{5}{125}=\log_{5}{(5)^3}\)
Use log rule: \(\log_{a}{(M)^k}=k.\log_{a}{M} →\log_{5}{(5)^3}=3\log_{5}{(5)}\)
Use log rule: \(\log_{a}{(a)} =1→ \log_{5}{(5)} =1.\)
\(3×3\log_{5}{(5)} =3×3=9\)
Evaluating Logarithm – Example 3:
Evaluate: \(\log_{10}{1000}\)
Solution:
Rewrite \(1000\) in power base form: \(1000=10^3\), then:
\(\log_{10}{1000}=\log_{10}{(10)^3}\)
Use log rule:\(\log_{a}{(M)^{k}}=k.\log_{a}{M}→\log_{10}{(10)^3}=3\log_{10}{(10)}\)
Use log rule: \(\log_{a}{(a)}=1→\log_{10}{(10)} =1.\)
\(3\log_{10}{(10)}=3×1=3\)
Evaluating Logarithm – Example 4:
Evaluate: \(5\log_{3}{81}\)
Solution:
Rewrite \(81\) in power base form: \(81=3^4\), then:
\(\log_{3}{81}=\log_{3}{(3)^4}\)
Use log rule: \(\log_{a}{(M)^k}=k.\log_{a}{M} →\log_{3}{(3)^4}=4\log_{3}{(3)}\)
Use log rule: \(\log_{a}{(a)} =1→ \log_{3}{(3)} =1.\)
\(5×4\log_{3}{(3)} =5×4=20\)
Exercises for Evaluating Logarithm
Evaluate Logarithm.
- \(\color{blue}{3\log_{2}{64}}\)
- \(\color{blue}{\frac{1}{2}\log_{6}{36}}\)
- \(\color{blue}{\frac{1}{3}\log_{3}{27}}\)
- \(\color{blue}{\log_{4}{64}}\)
- \(\color{blue}{\log_{1000}{1}}\)
- \(\color{blue}{\log_{620}{620}}\)
- \(\color{blue}{18}\)
- \(\color{blue}{1}\)
- \(\color{blue}{1}\)
- \(\color{blue}{3}\)
- \(\color{blue}{0}\)
- \(\color{blue}{1}\)
The Absolute Best Book for the Algebra Test
Related to This Article
More math articles
- ATI TEAS 7 Math FREE Sample Practice Questions
- Solving Percentage Word Problems
- Number Properties Puzzle – Challenge 21
- 5th Grade STAAR Math Practice Test Questions
- Long Division using 1 Number
- How to Apply Trigonometry: Practical Uses and Insights into Engineering and Astronomy
- 5th Grade NYSE Math Worksheets: FREE & Printable
- How to Use Division Properties
- 4th Grade Wisconsin Forward Math Worksheets: FREE & Printable
- 5th Grade STAAR Math FREE Sample Practice Questions
What people say about "How to Evaluate Logarithm? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.