# Connexions

You are here: Home » Content » Advanced Algebra II: Conceptual Explanations » The Logarithm Explained by Analogy to Roots

• How to Use Advanced Algebra II

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Bookshare

This collection is included inLens: Bookshare's Lens
By: Bookshare - A Benetech Initiative

"DAISY and BRF versions of this collection are available."

Click the "Bookshare" link to see all content affiliated with them.

• Featured Content

This collection is included inLens: Connexions Featured Content
By: Connexions

"This is the "concepts" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about […]"

Click the "Featured Content" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

#### Also in these lenses

• Busbee's Math Materials

This collection is included inLens: Busbee's Math Materials Lens
By: Kenneth Leroy Busbee

Click the "Busbee's Math Materials" link to see all content selected in this lens.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Inside Collection (Textbook):

Textbook by: Kenny M. Felder. E-mail the author

# The Logarithm Explained by Analogy to Roots

Module by: Kenny M. Felder. E-mail the author

Summary: This module discusses another way of understanding logarithms by providing an analogy to roots.

The logarithm may be the first really new concept you’ve encountered in Algebra II. So one of the easiest ways to understand it is by comparison with a familiar concept: roots.

Suppose someone asked you: “Exactly what does root mean?” You do understand roots, but they are difficult to define. After a few moments, you might come up with a definition very similar to the “question” definition of logarithms given above. 8383 size 12{ nroot { size 8{3} } {8} } {} means “what number cubed is 8?”

Now the person asks: “How do you find roots?” Well...you just play around with numbers until you find one that works. If someone asks for 2525 size 12{ sqrt {"25"} } {}, you just have to know that 52=2552=25 size 12{5 rSup { size 8{2} } ="25"} {}. If someone asks for 3030 size 12{ sqrt {"30"} } {}, you know that has to be bigger than 5 and smaller than 6; if you need more accuracy, it’s time for a calculator.

All that information about roots applies in a very analogous way to logarithms.

Table 1
Roots Logs
The question xaxa size 12{ nroot { size 8{a} } {x} } {} means “what number, raised to the a power, is x?” As an equation, ?a=x?a=x size 12{? rSup { size 8{a} } =x} {} logaxlogax size 12{"log" rSub { size 8{a} } x} {} means “ aa size 12{a} {}, raised to what power, is xx size 12{x} {}?” As an equation, a?=xa?=x size 12{a rSup { size 8{?} } =x} {}
Example that comes out even 8 3 = 2 8 3 = 2 size 12{ nroot { size 8{3} } {8} =2} {} log 2 8 = 3 log 2 8 = 3 size 12{"log" rSub { size 8{2} } 8=3} {}
Example that doesn’t 103103 size 12{ nroot { size 8{3} } {"10"} } {} is a bit more than 2 log210log210 size 12{"log" rSub { size 8{2} } "10"} {} is a bit more than 3
Out of domain example 44 size 12{ sqrt { - 4} } {}does not exist ( x2x2 size 12{x rSup { size 8{2} } } {} will never give 44 size 12{ - 4} {}) log2(0)log2(0) size 12{"log" rSub { size 8{2} } $$0$$ } {} and log2(1)log2(1) size 12{"log" rSub { size 8{2} } $$- 1$$ } {} do not exist ( 2x2x size 12{2 rSup { size 8{x} } } {} will never give 0 or a negative answer)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

#### Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

#### Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks