How to Evaluate Logarithms? (+FREE Worksheet!)

Do you want to know how to evaluate Logarithms? You can do it in a few easy steps!

How to Evaluate Logarithms? (+FREE Worksheet!)

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:

\(log_{b}{(x)}=\frac{log_{d}{(x)}}{\log_{d}{(b)}}\)
\(log_{a}{x^b}=b log_{a}{x}\)
\(log_{a}{1}=0\)
\(log_{a}{a}=1\)

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: \( 4log_{2}{2}=4\times1=4\)

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: \( 3 log_{4}{4}=3\times1=3\)

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.

  1. \(\color{blue}{log_{2}{\frac{1}{2}}}\)
  2. \(\color{blue}{log_{2}{\frac{1}{8}}}\)
  3. \(\color{blue}{log_{3}{\frac{1}{3}}}\)
  4. \(\color{blue}{log_{4}{\frac{1}{16}}}\)
  5. \(\color{blue}{log_{5}{25}}\)
  6. \(\color{blue}{log_{3}{27}}\)
  7. \(\color{blue}{log_{3}{9}}\)
  8. \(\color{blue}{log_{2}{32}}\)

Answers

  1. \(\color{blue}{-1}\)
  2. \(\color{blue}{-3}\)
  3. \(\color{blue}{-1}\)
  4. \(\color{blue}{-2}\)
  5. \(\color{blue}{2}\)
  6. \(\color{blue}{3}\)
  7. \(\color{blue}{2}\)
  8. \(\color{blue}{5}\)

Related to "How to Evaluate Logarithms? (+FREE Worksheet!)"

Managing Math Fear as an Adult
How to Handle Your Math Assignments?
How to Choose the Best Backup Software Solution for School Districts?
How to Find the Volume and Surface Area of a Triangular Pyramid?
How to Convert a Linear Equation in Standard Form to Slope-Intercept Form?
How to Find Values of Functions from Graphs?
How to Find the Unit Price of a Product?
How to Divide Decimals by Whole Numbers?
How to Find the Volume and Surface Area of Triangular Prism?
How to Find Elapsed Time?

What people say about "How to Evaluate Logarithms? (+FREE Worksheet!)"?

No one replied yet.

Leave a Reply

X
30% OFF

Huge Discount!

30% OFF

Take It Now!

SAVE $5

It was $16.99 now it is $11.99