56 lines
1.8 KiB
Markdown
56 lines
1.8 KiB
Markdown
---
|
|
title: Basic Log Rules and Expanding Log Expressions
|
|
---
|
|
## Basic Log Rules and Expanding Log Expressions
|
|
<!-- The article goes here, in GitHub-flavored Markdown. Feel free to add YouTube videos, images, and CodePen/JSBin embeds -->
|
|
|
|
The following are commonly used basic log rules:
|
|
|
|
###### Logarithm Product Rule
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (x * y) = log<sub>b</sub> (x) + log<sub>b</sub> (y) </span>
|
|
|
|
###### Logarithm Quotient Rule
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (x / y) = log<sub>b</sub> (x) - log<sub>b</sub> (y) </span>
|
|
|
|
###### Logarithm Power Rule</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (x<sup>y</sup>) = y * log<sub>b</sub> (x) </span>
|
|
|
|
###### Logarithm of Negative Number</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (x) </span> is undefined when <span class="texhtml"> x < 0 </span>
|
|
|
|
###### Logarithm of 0</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (0) </span> is undefined
|
|
|
|
<span class="texhtml"> lim<sub>x → 0+</sub> log<sub>b</sub> (x) = -infinity </span>
|
|
|
|
###### Logarithm of 1</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (1) = 0 </span>
|
|
|
|
###### Logarithm of the Base</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (b) = 1 </span>
|
|
|
|
###### Logarithm of Infinity</strong>
|
|
|
|
<span class="texhtml"> lim<sub> x → infinity</sub> log<sub>b</sub> (x) = infinity </span>
|
|
|
|
###### Logarithm Base Switch Rule</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (c) = 1 / log<sub>c</sub> (b) </span>
|
|
|
|
###### Logarithm Base Change Rule</strong>
|
|
|
|
<span class="texhtml"> log<sub>b</sub> (x) = log<sub>c</sub> (x) / log<sub>c</sub> (b) </span>
|
|
|
|
#### More Information:
|
|
<!-- Please add any articles you think might be helpful to read before writing the article -->
|
|
|
|
<a href='http://www.rapidtables.com/math/algebra/Logarithm.htm' target='_blank' rel='nofollow'>Logarithm Rules</a>
|
|
|